3.4.97 \(\int x (a+b \log (c (d+e x)^n))^3 (f+g \log (h (i+j x)^m)) \, dx\) [397]

Optimal. Leaf size=2050 \[ \text {result too large to display} \]

[Out]

12*b^3*d*g*m*n^2*(e*x+d)*ln(c*(e*x+d)^n)/e^2-15/4*b*d*g*m*n*(e*x+d)*(a+b*ln(c*(e*x+d)^n))^2/e^2-3/4*b^2*g*i^2*
m*n^2*(a+b*ln(c*(e*x+d)^n))*ln(e*(j*x+i)/(-d*j+e*i))/j^2-9/4*b*d^2*g*m*n*(a+b*ln(c*(e*x+d)^n))^2*ln(e*(j*x+i)/
(-d*j+e*i))/e^2-9/2*b^2*d*g*i*m*n^2*(a+b*ln(c*(e*x+d)^n))*ln(e*(j*x+i)/(-d*j+e*i))/e/j+3/2*b*d*g*i*m*n*(a+b*ln
(c*(e*x+d)^n))^2*ln(e*(j*x+i)/(-d*j+e*i))/e/j+3*b^2*d*g*i*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(2,-j*(e*x+d)/(-d
*j+e*i))/e/j-1/4*g*m*(e*x+d)^2*(a+b*ln(c*(e*x+d)^n))^3/e^2-3/8*b^3*g*n^3*x^2*ln(h*(j*x+i)^m)-1/2*d^2*g*(a+b*ln
(c*(e*x+d)^n))^3*ln(h*(j*x+i)^m)/e^2-1/2*d^2*f*(a+b*ln(c*(e*x+d)^n))^3/e^2+3/8*b^3*g*m*n^3*x^2-3/8*b^3*f*n^3*(
e*x+d)^2/e^2+3/4*b*g*i^2*m*n*(a+b*ln(c*(e*x+d)^n))^2*ln(e*(j*x+i)/(-d*j+e*i))/j^2+21/4*b^3*d*g*n^3*(j*x+i)*ln(
h*(j*x+i)^m)/e/j-9/2*b^2*d*g*n^2*x*(a+b*ln(c*(e*x+d)^n))*ln(h*(j*x+i)^m)/e+3/2*b*d*g*n*x*(a+b*ln(c*(e*x+d)^n))
^2*ln(h*(j*x+i)^m)/e-9/2*b^2*d^2*g*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(2,-j*(e*x+d)/(-d*j+e*i))/e^2+3/2*b^2*g*
i^2*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(2,-j*(e*x+d)/(-d*j+e*i))/j^2+3/2*b*d^2*g*m*n*(a+b*ln(c*(e*x+d)^n))^2*p
olylog(2,-j*(e*x+d)/(-d*j+e*i))/e^2-3/2*b*g*i^2*m*n*(a+b*ln(c*(e*x+d)^n))^2*polylog(2,-j*(e*x+d)/(-d*j+e*i))/j
^2-3*b^2*d^2*g*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(3,-j*(e*x+d)/(-d*j+e*i))/e^2+3*b^2*g*i^2*m*n^2*(a+b*ln(c*(e
*x+d)^n))*polylog(3,-j*(e*x+d)/(-d*j+e*i))/j^2+1/2*x^2*(a+b*ln(c*(e*x+d)^n))^3*(f+g*ln(h*(j*x+i)^m))-3/4*b^3*g
*i^2*m*n^3*polylog(2,-j*(e*x+d)/(-d*j+e*i))/j^2-21/4*b^3*d^2*g*m*n^3*polylog(2,e*(j*x+i)/(-d*j+e*i))/e^2+9/2*b
^3*d^2*g*m*n^3*polylog(3,-j*(e*x+d)/(-d*j+e*i))/e^2-3/2*b^3*g*i^2*m*n^3*polylog(3,-j*(e*x+d)/(-d*j+e*i))/j^2+3
*b^3*d^2*g*m*n^3*polylog(4,-j*(e*x+d)/(-d*j+e*i))/e^2-3*b^3*g*i^2*m*n^3*polylog(4,-j*(e*x+d)/(-d*j+e*i))/j^2-6
*a*b^2*d*f*n^2*x/e-141/8*b^3*d*g*m*n^3*x/e-45/8*b^3*g*i*m*n^3*x/j-3/8*b^2*g*m*n^2*x^2*(a+b*ln(c*(e*x+d)^n))+3/
4*b^2*f*n^2*(e*x+d)^2*(a+b*ln(c*(e*x+d)^n))/e^2-3/4*b*f*n*(e*x+d)^2*(a+b*ln(c*(e*x+d)^n))^2/e^2+1/2*d*g*m*(e*x
+d)*(a+b*ln(c*(e*x+d)^n))^3/e^2-3*b^3*d*g*i*m*n^3*polylog(3,-j*(e*x+d)/(-d*j+e*i))/e/j-9/2*b^3*d*g*i*m*n^3*pol
ylog(2,-j*(e*x+d)/(-d*j+e*i))/e/j+6*b^3*d*f*n^3*x/e+3/8*b^3*g*m*n^3*(e*x+d)^2/e^2+21/4*b^3*g*i*m*n^2*(e*x+d)*l
n(c*(e*x+d)^n)/e/j-9/4*b*g*i*m*n*(e*x+d)*(a+b*ln(c*(e*x+d)^n))^2/e/j+1/2*d^2*g*m*(a+b*ln(c*(e*x+d)^n))^3*ln(e*
(j*x+i)/(-d*j+e*i))/e^2-1/2*g*i^2*m*(a+b*ln(c*(e*x+d)^n))^3*ln(e*(j*x+i)/(-d*j+e*i))/j^2+3/4*b^2*g*n^2*x^2*(a+
b*ln(c*(e*x+d)^n))*ln(h*(j*x+i)^m)-3/4*b*g*n*x^2*(a+b*ln(c*(e*x+d)^n))^2*ln(h*(j*x+i)^m)+9/4*b*d^2*g*n*(a+b*ln
(c*(e*x+d)^n))^2*ln(h*(j*x+i)^m)/e^2+3/8*b^3*d^2*g*m*n^3*ln(e*x+d)/e^2-6*b^3*d*f*n^2*(e*x+d)*ln(c*(e*x+d)^n)/e
^2-3/4*b^2*g*m*n^2*(e*x+d)^2*(a+b*ln(c*(e*x+d)^n))/e^2+3*b*d*f*n*(e*x+d)*(a+b*ln(c*(e*x+d)^n))^2/e^2+3/4*b*g*m
*n*(e*x+d)^2*(a+b*ln(c*(e*x+d)^n))^2/e^2+1/2*g*i*m*(e*x+d)*(a+b*ln(c*(e*x+d)^n))^3/e/j+3/8*b^3*g*i^2*m*n^3*ln(
j*x+i)/j^2-21/4*b^3*d^2*g*n^3*ln(-j*(e*x+d)/(-d*j+e*i))*ln(h*(j*x+i)^m)/e^2+21/4*a*b^2*g*i*m*n^2*x/j+12*a*b^2*
d*g*m*n^2*x/e

________________________________________________________________________________________

Rubi [A]
time = 4.81, antiderivative size = 2050, normalized size of antiderivative = 1.00, number of steps used = 148, number of rules used = 32, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 1.000, Rules used = {2489, 2463, 2436, 2333, 2332, 2448, 2437, 2342, 2341, 2443, 2481, 2421, 2430, 6724, 6874, 2458, 2388, 2339, 30, 2367, 2479, 2338, 45, 2441, 2440, 2438, 2422, 2354, 2372, 12, 14, 2442} \begin {gather*} \frac {3}{8} g m n^3 x^2 b^3-\frac {3 f n^3 (d+e x)^2 b^3}{8 e^2}+\frac {3 g m n^3 (d+e x)^2 b^3}{8 e^2}+\frac {6 d f n^3 x b^3}{e}-\frac {141 d g m n^3 x b^3}{8 e}-\frac {45 g i m n^3 x b^3}{8 j}+\frac {3 d^2 g m n^3 \log (d+e x) b^3}{8 e^2}-\frac {6 d f n^2 (d+e x) \log \left (c (d+e x)^n\right ) b^3}{e^2}+\frac {12 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right ) b^3}{e^2}+\frac {21 g i m n^2 (d+e x) \log \left (c (d+e x)^n\right ) b^3}{4 e j}+\frac {3 g i^2 m n^3 \log (i+j x) b^3}{8 j^2}-\frac {3}{8} g n^3 x^2 \log \left (h (i+j x)^m\right ) b^3+\frac {21 d g n^3 (i+j x) \log \left (h (i+j x)^m\right ) b^3}{4 e j}-\frac {21 d^2 g n^3 \log \left (-\frac {j (d+e x)}{e i-d j}\right ) \log \left (h (i+j x)^m\right ) b^3}{4 e^2}-\frac {9 d g i m n^3 \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{2 e j}-\frac {3 g i^2 m n^3 \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{4 j^2}-\frac {21 d^2 g m n^3 \text {PolyLog}\left (2,\frac {e (i+j x)}{e i-d j}\right ) b^3}{4 e^2}+\frac {9 d^2 g m n^3 \text {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{2 e^2}-\frac {3 d g i m n^3 \text {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{e j}-\frac {3 g i^2 m n^3 \text {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{2 j^2}+\frac {3 d^2 g m n^3 \text {PolyLog}\left (4,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{e^2}-\frac {3 g i^2 m n^3 \text {PolyLog}\left (4,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{j^2}-\frac {6 a d f n^2 x b^2}{e}+\frac {12 a d g m n^2 x b^2}{e}+\frac {21 a g i m n^2 x b^2}{4 j}-\frac {3}{8} g m n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) b^2+\frac {3 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) b^2}{4 e^2}-\frac {3 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) b^2}{4 e^2}-\frac {9 d g i m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (i+j x)}{e i-d j}\right ) b^2}{2 e j}-\frac {3 g i^2 m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (i+j x)}{e i-d j}\right ) b^2}{4 j^2}+\frac {3}{4} g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (i+j x)^m\right ) b^2-\frac {9 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (i+j x)^m\right ) b^2}{2 e}-\frac {9 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b^2}{2 e^2}+\frac {3 d g i m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b^2}{e j}+\frac {3 g i^2 m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b^2}{2 j^2}-\frac {3 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) b^2}{e^2}+\frac {3 g i^2 m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) b^2}{j^2}-\frac {3 f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 b}{4 e^2}+\frac {3 g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 b}{4 e^2}+\frac {3 d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2 b}{e^2}-\frac {15 d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2 b}{4 e^2}-\frac {9 g i m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2 b}{4 e j}-\frac {9 d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (i+j x)}{e i-d j}\right ) b}{4 e^2}+\frac {3 d g i m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (i+j x)}{e i-d j}\right ) b}{2 e j}+\frac {3 g i^2 m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (i+j x)}{e i-d j}\right ) b}{4 j^2}-\frac {3}{4} g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (i+j x)^m\right ) b+\frac {9 d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (i+j x)^m\right ) b}{4 e^2}+\frac {3 d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (i+j x)^m\right ) b}{2 e}+\frac {3 d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b}{2 e^2}-\frac {3 g i^2 m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b}{2 j^2}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {g i m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (i+j x)}{e i-d j}\right )}{2 e^2}-\frac {g i^2 m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (i+j x)}{e i-d j}\right )}{2 j^2}-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (i+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[x*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]),x]

[Out]

(-6*a*b^2*d*f*n^2*x)/e + (12*a*b^2*d*g*m*n^2*x)/e + (21*a*b^2*g*i*m*n^2*x)/(4*j) + (6*b^3*d*f*n^3*x)/e - (141*
b^3*d*g*m*n^3*x)/(8*e) - (45*b^3*g*i*m*n^3*x)/(8*j) + (3*b^3*g*m*n^3*x^2)/8 - (3*b^3*f*n^3*(d + e*x)^2)/(8*e^2
) + (3*b^3*g*m*n^3*(d + e*x)^2)/(8*e^2) + (3*b^3*d^2*g*m*n^3*Log[d + e*x])/(8*e^2) - (6*b^3*d*f*n^2*(d + e*x)*
Log[c*(d + e*x)^n])/e^2 + (12*b^3*d*g*m*n^2*(d + e*x)*Log[c*(d + e*x)^n])/e^2 + (21*b^3*g*i*m*n^2*(d + e*x)*Lo
g[c*(d + e*x)^n])/(4*e*j) - (3*b^2*g*m*n^2*x^2*(a + b*Log[c*(d + e*x)^n]))/8 + (3*b^2*f*n^2*(d + e*x)^2*(a + b
*Log[c*(d + e*x)^n]))/(4*e^2) - (3*b^2*g*m*n^2*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n]))/(4*e^2) + (3*b*d*f*n*(d
+ e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^2 - (15*b*d*g*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) - (9
*b*g*i*m*n*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/(4*e*j) - (3*b*f*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2
)/(4*e^2) + (3*b*g*m*n*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^2)/(4*e^2) - (d^2*f*(a + b*Log[c*(d + e*x)^n])^3
)/(2*e^2) + (d*g*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^3)/(2*e^2) + (g*i*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n
])^3)/(2*e*j) - (g*m*(d + e*x)^2*(a + b*Log[c*(d + e*x)^n])^3)/(4*e^2) + (3*b^3*g*i^2*m*n^3*Log[i + j*x])/(8*j
^2) - (3*b^2*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(4*j^2) - (9*b^2*d*g*i*m*n
^2*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e*j) - (9*b*d^2*g*m*n*(a + b*Log[c*(d + e*x)^
n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(4*e^2) + (3*b*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/
(e*i - d*j)])/(4*j^2) + (3*b*d*g*i*m*n*(a + b*Log[c*(d + e*x)^n])^2*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e*j) +
(d^2*g*m*(a + b*Log[c*(d + e*x)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/(2*e^2) - (g*i^2*m*(a + b*Log[c*(d + e*x
)^n])^3*Log[(e*(i + j*x))/(e*i - d*j)])/(2*j^2) - (3*b^3*g*n^3*x^2*Log[h*(i + j*x)^m])/8 + (21*b^3*d*g*n^3*(i
+ j*x)*Log[h*(i + j*x)^m])/(4*e*j) - (21*b^3*d^2*g*n^3*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*(i + j*x)^m])/(
4*e^2) - (9*b^2*d*g*n^2*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m])/(2*e) + (3*b^2*g*n^2*x^2*(a + b*Log[c
*(d + e*x)^n])*Log[h*(i + j*x)^m])/4 + (9*b*d^2*g*n*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(4*e^2) +
(3*b*d*g*n*x*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/(2*e) - (3*b*g*n*x^2*(a + b*Log[c*(d + e*x)^n])
^2*Log[h*(i + j*x)^m])/4 - (d^2*g*(a + b*Log[c*(d + e*x)^n])^3*Log[h*(i + j*x)^m])/(2*e^2) + (x^2*(a + b*Log[c
*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]))/2 - (3*b^3*g*i^2*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/
(4*j^2) - (9*b^3*d*g*i*m*n^3*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*e*j) - (9*b^2*d^2*g*m*n^2*(a + b*Log
[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*e^2) + (3*b^2*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)
^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(2*j^2) + (3*b^2*d*g*i*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyLog
[2, -((j*(d + e*x))/(e*i - d*j))])/(e*j) + (3*b*d^2*g*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*
x))/(e*i - d*j))])/(2*e^2) - (3*b*g*i^2*m*n*(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j
))])/(2*j^2) - (21*b^3*d^2*g*m*n^3*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/(4*e^2) + (9*b^3*d^2*g*m*n^3*PolyLog
[3, -((j*(d + e*x))/(e*i - d*j))])/(2*e^2) - (3*b^3*g*i^2*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(2*j
^2) - (3*b^3*d*g*i*m*n^3*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/(e*j) - (3*b^2*d^2*g*m*n^2*(a + b*Log[c*(d
+ e*x)^n])*PolyLog[3, -((j*(d + e*x))/(e*i - d*j))])/e^2 + (3*b^2*g*i^2*m*n^2*(a + b*Log[c*(d + e*x)^n])*PolyL
og[3, -((j*(d + e*x))/(e*i - d*j))])/j^2 + (3*b^3*d^2*g*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/e^2 -
(3*b^3*g*i^2*m*n^3*PolyLog[4, -((j*(d + e*x))/(e*i - d*j))])/j^2

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rule 45

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])

Rule 2332

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 2333

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.), x_Symbol] :> Simp[x*(a + b*Log[c*x^n])^p, x] - Dist[b*n*p, In
t[(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{a, b, c, n}, x] && GtQ[p, 0] && IntegerQ[2*p]

Rule 2338

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))/(x_), x_Symbol] :> Simp[(a + b*Log[c*x^n])^2/(2*b*n), x] /; FreeQ[{a
, b, c, n}, x]

Rule 2339

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/(x_), x_Symbol] :> Dist[1/(b*n), Subst[Int[x^p, x], x, a + b*L
og[c*x^n]], x] /; FreeQ[{a, b, c, n, p}, x]

Rule 2341

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Log[c*x^
n])/(d*(m + 1))), x] - Simp[b*n*((d*x)^(m + 1)/(d*(m + 1)^2)), x] /; FreeQ[{a, b, c, d, m, n}, x] && NeQ[m, -1
]

Rule 2342

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_.)*(x_))^(m_.), x_Symbol] :> Simp[(d*x)^(m + 1)*((a + b*Lo
g[c*x^n])^p/(d*(m + 1))), x] - Dist[b*n*(p/(m + 1)), Int[(d*x)^m*(a + b*Log[c*x^n])^(p - 1), x], x] /; FreeQ[{
a, b, c, d, m, n}, x] && NeQ[m, -1] && GtQ[p, 0]

Rule 2354

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)/((d_) + (e_.)*(x_)), x_Symbol] :> Simp[Log[1 + e*(x/d)]*((a +
b*Log[c*x^n])^p/e), x] - Dist[b*n*(p/e), Int[Log[1 + e*(x/d)]*((a + b*Log[c*x^n])^(p - 1)/x), x], x] /; FreeQ[
{a, b, c, d, e, n}, x] && IGtQ[p, 0]

Rule 2367

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = Expand
Integrand[(a + b*Log[c*x^n])^p, (d + e*x^r)^q, x]}, Int[u, x] /; SumQ[u]] /; FreeQ[{a, b, c, d, e, n, p, q, r}
, x] && IntegerQ[q] && (GtQ[q, 0] || (IGtQ[p, 0] && IntegerQ[r]))

Rule 2372

Int[((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))*(x_)^(m_.)*((d_) + (e_.)*(x_)^(r_.))^(q_.), x_Symbol] :> With[{u = I
ntHide[x^m*(d + e*x^r)^q, x]}, Dist[a + b*Log[c*x^n], u, x] - Dist[b*n, Int[SimplifyIntegrand[u/x, x], x], x]]
/; FreeQ[{a, b, c, d, e, n, r}, x] && IGtQ[q, 0] && IntegerQ[m] &&  !(EqQ[q, 1] && EqQ[m, -1])

Rule 2388

Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*((d_) + (e_.)*(x_))^(q_.))/(x_), x_Symbol] :> Dist[d, Int[(d
+ e*x)^(q - 1)*((a + b*Log[c*x^n])^p/x), x], x] + Dist[e, Int[(d + e*x)^(q - 1)*(a + b*Log[c*x^n])^p, x], x] /
; FreeQ[{a, b, c, d, e, n}, x] && IGtQ[p, 0] && GtQ[q, 0] && IntegerQ[2*q]

Rule 2421

Int[(Log[(d_.)*((e_) + (f_.)*(x_)^(m_.))]*((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.))/(x_), x_Symbol] :> Simp
[(-PolyLog[2, (-d)*f*x^m])*((a + b*Log[c*x^n])^p/m), x] + Dist[b*n*(p/m), Int[PolyLog[2, (-d)*f*x^m]*((a + b*L
og[c*x^n])^(p - 1)/x), x], x] /; FreeQ[{a, b, c, d, e, f, m, n}, x] && IGtQ[p, 0] && EqQ[d*e, 1]

Rule 2422

Int[(Log[(d_.)*((e_) + (f_.)*(x_)^(m_.))^(r_.)]*((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.))/(x_), x_Symbol] :
> Simp[Log[d*(e + f*x^m)^r]*((a + b*Log[c*x^n])^(p + 1)/(b*n*(p + 1))), x] - Dist[f*m*(r/(b*n*(p + 1))), Int[x
^(m - 1)*((a + b*Log[c*x^n])^(p + 1)/(e + f*x^m)), x], x] /; FreeQ[{a, b, c, d, e, f, r, m, n}, x] && IGtQ[p,
0] && NeQ[d*e, 1]

Rule 2430

Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*PolyLog[k_, (e_.)*(x_)^(q_.)])/(x_), x_Symbol] :> Simp[PolyLo
g[k + 1, e*x^q]*((a + b*Log[c*x^n])^p/q), x] - Dist[b*n*(p/q), Int[PolyLog[k + 1, e*x^q]*((a + b*Log[c*x^n])^(
p - 1)/x), x], x] /; FreeQ[{a, b, c, e, k, n, q}, x] && GtQ[p, 0]

Rule 2436

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.), x_Symbol] :> Dist[1/e, Subst[Int[(a + b*Log[c*
x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, n, p}, x]

Rule 2437

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_) + (g_.)*(x_))^(q_.), x_Symbol] :> Dist[1/
e, Subst[Int[(f*(x/d))^q*(a + b*Log[c*x^n])^p, x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p, q}, x]
&& EqQ[e*f - d*g, 0]

Rule 2438

Int[Log[(c_.)*((d_) + (e_.)*(x_)^(n_.))]/(x_), x_Symbol] :> Simp[-PolyLog[2, (-c)*e*x^n]/n, x] /; FreeQ[{c, d,
e, n}, x] && EqQ[c*d, 1]

Rule 2440

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))]*(b_.))/((f_.) + (g_.)*(x_)), x_Symbol] :> Dist[1/g, Subst[Int[(a +
b*Log[1 + c*e*(x/g)])/x, x], x, f + g*x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[e*f - d*g, 0] && EqQ[g
+ c*(e*f - d*g), 0]

Rule 2441

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))/((f_.) + (g_.)*(x_)), x_Symbol] :> Simp[Log[e*((f + g
*x)/(e*f - d*g))]*((a + b*Log[c*(d + e*x)^n])/g), x] - Dist[b*e*(n/g), Int[Log[(e*(f + g*x))/(e*f - d*g)]/(d +
e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n}, x] && NeQ[e*f - d*g, 0]

Rule 2442

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Simp[(f + g*
x)^(q + 1)*((a + b*Log[c*(d + e*x)^n])/(g*(q + 1))), x] - Dist[b*e*(n/(g*(q + 1))), Int[(f + g*x)^(q + 1)/(d +
e*x), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, q}, x] && NeQ[e*f - d*g, 0] && NeQ[q, -1]

Rule 2443

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)/((f_.) + (g_.)*(x_)), x_Symbol] :> Simp[Log[e*((
f + g*x)/(e*f - d*g))]*((a + b*Log[c*(d + e*x)^n])^p/g), x] - Dist[b*e*n*(p/g), Int[Log[(e*(f + g*x))/(e*f - d
*g)]*((a + b*Log[c*(d + e*x)^n])^(p - 1)/(d + e*x)), x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p}, x] && NeQ[e*
f - d*g, 0] && IGtQ[p, 1]

Rule 2448

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_)*((f_.) + (g_.)*(x_))^(q_.), x_Symbol] :> Int[Exp
andIntegrand[(f + g*x)^q*(a + b*Log[c*(d + e*x)^n])^p, x], x] /; FreeQ[{a, b, c, d, e, f, g, n, p}, x] && NeQ[
e*f - d*g, 0] && IGtQ[q, 0]

Rule 2458

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + (g_.)*(x_))^(q_.)*((h_.) + (i_.)*(x_))
^(r_.), x_Symbol] :> Dist[1/e, Subst[Int[(g*(x/e))^q*((e*h - d*i)/e + i*(x/e))^r*(a + b*Log[c*x^n])^p, x], x,
d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, h, i, n, p, q, r}, x] && EqQ[e*f - d*g, 0] && (IGtQ[p, 0] || IGtQ[
r, 0]) && IntegerQ[2*r]

Rule 2463

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((h_.)*(x_))^(m_.)*((f_) + (g_.)*(x_)^(r_.))^(q
_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*Log[c*(d + e*x)^n])^p, (h*x)^m*(f + g*x^r)^q, x], x] /; FreeQ[{a,
b, c, d, e, f, g, h, m, n, p, q, r}, x] && IntegerQ[m] && IntegerQ[q]

Rule 2479

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + Log[(h_.)*((i_.) + (j_.)*(x_))^(m_.)]*
(g_.)), x_Symbol] :> Simp[x*(a + b*Log[c*(d + e*x)^n])^p*(f + g*Log[h*(i + j*x)^m]), x] + (-Dist[g*j*m, Int[x*
((a + b*Log[c*(d + e*x)^n])^p/(i + j*x)), x], x] - Dist[b*e*n*p, Int[x*(a + b*Log[c*(d + e*x)^n])^(p - 1)*((f
+ g*Log[h*(i + j*x)^m])/(d + e*x)), x], x]) /; FreeQ[{a, b, c, d, e, f, g, h, i, j, m, n}, x] && IGtQ[p, 0]

Rule 2481

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + Log[(h_.)*((i_.) + (j_.)*(x_))^(m_.)]*
(g_.))*((k_.) + (l_.)*(x_))^(r_.), x_Symbol] :> Dist[1/e, Subst[Int[(k*(x/d))^r*(a + b*Log[c*x^n])^p*(f + g*Lo
g[h*((e*i - d*j)/e + j*(x/e))^m]), x], x, d + e*x], x] /; FreeQ[{a, b, c, d, e, f, g, h, i, j, k, l, n, p, r},
x] && EqQ[e*k - d*l, 0]

Rule 2489

Int[((a_.) + Log[(c_.)*((d_) + (e_.)*(x_))^(n_.)]*(b_.))^(p_.)*((f_.) + Log[(h_.)*((i_.) + (j_.)*(x_))^(m_.)]*
(g_.))*(x_)^(r_.), x_Symbol] :> Simp[x^(r + 1)*(a + b*Log[c*(d + e*x)^n])^p*((f + g*Log[h*(i + j*x)^m])/(r + 1
)), x] + (-Dist[g*j*(m/(r + 1)), Int[x^(r + 1)*((a + b*Log[c*(d + e*x)^n])^p/(i + j*x)), x], x] - Dist[b*e*n*(
p/(r + 1)), Int[x^(r + 1)*(a + b*Log[c*(d + e*x)^n])^(p - 1)*((f + g*Log[h*(i + j*x)^m])/(d + e*x)), x], x]) /
; FreeQ[{a, b, c, d, e, f, g, h, i, j, m, n}, x] && IGtQ[p, 0] && IntegerQ[r] && (EqQ[p, 1] || GtQ[r, 0]) && N
eQ[r, -1]

Rule 6724

Int[PolyLog[n_, (c_.)*((a_.) + (b_.)*(x_))^(p_.)]/((d_.) + (e_.)*(x_)), x_Symbol] :> Simp[PolyLog[n + 1, c*(a
+ b*x)^p]/(e*p), x] /; FreeQ[{a, b, c, d, e, n, p}, x] && EqQ[b*d, a*e]

Rule 6874

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {align*} \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right ) \, dx &=\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {1}{2} (g j m) \int \frac {x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{397+j x} \, dx-\frac {1}{2} (3 b e n) \int \frac {x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (397+j x)^m\right )\right )}{d+e x} \, dx\\ &=\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {1}{2} (g j m) \int \left (-\frac {397 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j^2}+\frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j}+\frac {157609 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j^2 (397+j x)}\right ) \, dx-\frac {1}{2} (3 b e n) \int \left (\frac {f x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{d+e x}+\frac {g x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{d+e x}\right ) \, dx\\ &=\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {1}{2} (g m) \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx+\frac {(397 g m) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx}{2 j}-\frac {(157609 g m) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3}{397+j x} \, dx}{2 j}-\frac {1}{2} (3 b e f n) \int \frac {x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{d+e x} \, dx-\frac {1}{2} (3 b e g n) \int \frac {x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{d+e x} \, dx\\ &=-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {1}{2} (g m) \int \left (-\frac {d \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{e}+\frac {(d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{e}\right ) \, dx+\frac {(397 g m) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^3 \, dx,x,d+e x\right )}{2 e j}-\frac {1}{2} (3 b f n) \text {Subst}\left (\int \frac {\left (-\frac {d}{e}+\frac {x}{e}\right )^2 \left (a+b \log \left (c x^n\right )\right )^2}{x} \, dx,x,d+e x\right )-\frac {1}{2} (3 b e g n) \int \left (-\frac {d \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{e^2}+\frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{e}+\frac {d^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{e^2 (d+e x)}\right ) \, dx+\frac {(472827 b e g m n) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{2 j^2}\\ &=\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {(g m) \int (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx}{2 e}+\frac {(d g m) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \, dx}{2 e}-\frac {(3 b f n) \text {Subst}\left (\int \left (-\frac {d}{e}+\frac {x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e}+\frac {(3 b d f n) \text {Subst}\left (\int \frac {\left (-\frac {d}{e}+\frac {x}{e}\right ) \left (a+b \log \left (c x^n\right )\right )^2}{x} \, dx,x,d+e x\right )}{2 e}-\frac {1}{2} (3 b g n) \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right ) \, dx+\frac {(3 b d g n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right ) \, dx}{2 e}-\frac {\left (3 b d^2 g n\right ) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{d+e x} \, dx}{2 e}+\frac {(472827 b g m n) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \log \left (\frac {e \left (\frac {397 e-d j}{e}+\frac {j x}{e}\right )}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 j^2}-\frac {(1191 b g m n) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e j}\\ &=-\frac {1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {(g m) \text {Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^3 \, dx,x,d+e x\right )}{2 e^2}+\frac {(d g m) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^3 \, dx,x,d+e x\right )}{2 e^2}+\frac {(3 b d f n) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}-\frac {\left (3 b d^2 f n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{x} \, dx,x,d+e x\right )}{2 e^2}-\frac {(3 b f n) \text {Subst}\left (\int \left (-\frac {d \left (a+b \log \left (c x^n\right )\right )^2}{e}+\frac {x \left (a+b \log \left (c x^n\right )\right )^2}{e}\right ) \, dx,x,d+e x\right )}{2 e}-\frac {\left (3 b d^2 g n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \log \left (h \left (\frac {397 e-d j}{e}+\frac {j x}{e}\right )^m\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac {1}{4} (3 b g j m n) \int \frac {x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx-\frac {(3 b d g j m n) \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx}{2 e}-\left (3 b^2 d g n^2\right ) \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx+\frac {1}{2} \left (3 b^2 e g n^2\right ) \int \frac {x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx+\frac {\left (472827 b^2 g m n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{j^2}+\frac {\left (1191 b^2 g m n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e j}\\ &=\frac {1191 a b^2 g m n^2 x}{j}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e^2}-\frac {1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}-\frac {\left (3 d^2 f\right ) \text {Subst}\left (\int x^2 \, dx,x,a+b \log \left (c (d+e x)^n\right )\right )}{2 e^2}+\frac {\left (d^2 g j m\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^3}{\frac {397 e-d j}{e}+\frac {j x}{e}} \, dx,x,d+e x\right )}{2 e^3}-\frac {(3 b f n) \text {Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}+\frac {(3 b d f n) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}+\frac {(3 b g m n) \text {Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e^2}-\frac {(3 b d g m n) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}+\frac {1}{4} (3 b g j m n) \int \left (-\frac {397 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j^2}+\frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j}+\frac {157609 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j^2 (397+j x)}\right ) \, dx-\frac {(3 b d g j m n) \int \left (\frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j}-\frac {397 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j (397+j x)}\right ) \, dx}{2 e}-\frac {\left (3 b^2 d f n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}-\left (3 b^2 d g n^2\right ) \int \left (\frac {\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e}-\frac {d \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e (d+e x)}\right ) \, dx+\frac {1}{2} \left (3 b^2 e g n^2\right ) \int \left (-\frac {d \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e^2}+\frac {x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e}+\frac {d^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{e^2 (d+e x)}\right ) \, dx+\frac {\left (1191 b^3 g m n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e j}-\frac {\left (472827 b^3 g m n^3\right ) \text {Subst}\left (\int \frac {\text {Li}_3\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{j^2}\\ &=-\frac {3 a b^2 d f n^2 x}{e}+\frac {1191 a b^2 g m n^2 x}{j}-\frac {1191 b^3 g m n^3 x}{j}+\frac {1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e^2}-\frac {1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}-\frac {3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac {3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}-\frac {472827 b^3 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {1}{4} (3 b g m n) \int x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx-\frac {\left (3 b d^2 g m n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \log \left (1+\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e^2}-\frac {(3 b d g m n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{2 e}+\frac {(1191 b d g m n) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx}{2 e}-\frac {(1191 b g m n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{4 j}+\frac {(472827 b g m n) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^2}{397+j x} \, dx}{4 j}+\frac {\left (3 b^2 f n^2\right ) \text {Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{2 e^2}-\frac {\left (3 b^2 d f n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}-\frac {\left (3 b^3 d f n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac {1}{2} \left (3 b^2 g n^2\right ) \int x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right ) \, dx-\frac {\left (3 b^2 d g n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right ) \, dx}{2 e}-\frac {\left (3 b^2 d g n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right ) \, dx}{e}+\frac {\left (3 b^2 d^2 g n^2\right ) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx}{2 e}+\frac {\left (3 b^2 d^2 g n^2\right ) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{d+e x} \, dx}{e}-\frac {\left (3 b^2 g m n^2\right ) \text {Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{4 e^2}+\frac {\left (3 b^2 d g m n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}\\ &=-\frac {6 a b^2 d f n^2 x}{e}+\frac {3 a b^2 d g m n^2 x}{e}+\frac {1191 a b^2 g m n^2 x}{j}+\frac {3 b^3 d f n^3 x}{e}-\frac {1191 b^3 g m n^3 x}{j}-\frac {3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac {3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac {3 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac {3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac {3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e^2}-\frac {1191 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{2 e j}-\frac {3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac {3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac {1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac {9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac {3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac {3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}-\frac {472827 b^3 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {1}{4} (3 b g m n) \int \left (-\frac {d \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e}+\frac {(d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e}\right ) \, dx-\frac {(3 b d g m n) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{2 e^2}-\frac {(1191 b g m n) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e j}-\frac {\left (3 b^3 d f n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac {\left (3 b^2 d^2 g n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (h \left (\frac {397 e-d j}{e}+\frac {j x}{e}\right )^m\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac {\left (3 b^2 d^2 g n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (h \left (\frac {397 e-d j}{e}+\frac {j x}{e}\right )^m\right )}{x} \, dx,x,d+e x\right )}{e^2}+\frac {\left (3 b^3 d g m n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}-\frac {\left (3 b^2 d^2 g m n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \text {Li}_2\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}-\frac {\left (472827 b^2 e g m n^2\right ) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{2 j^2}-\frac {\left (1191 b^2 d g m n^2\right ) \int \frac {\left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{j}-\frac {1}{4} \left (3 b^2 g j m n^2\right ) \int \frac {x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{397+j x} \, dx+\frac {\left (3 b^2 d g j m n^2\right ) \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )}{397+j x} \, dx}{2 e}+\frac {\left (3 b^2 d g j m n^2\right ) \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )}{397+j x} \, dx}{e}+\frac {1}{2} \left (3 b^3 d g n^3\right ) \int \frac {x \log \left (h (397+j x)^m\right )}{d+e x} \, dx+\left (3 b^3 d g n^3\right ) \int \frac {x \log \left (h (397+j x)^m\right )}{d+e x} \, dx-\frac {1}{4} \left (3 b^3 e g n^3\right ) \int \frac {x^2 \log \left (h (397+j x)^m\right )}{d+e x} \, dx\\ &=-\frac {6 a b^2 d f n^2 x}{e}+\frac {3 a b^2 d g m n^2 x}{e}+\frac {1191 a b^2 g m n^2 x}{j}+\frac {6 b^3 d f n^3 x}{e}-\frac {3 b^3 d g m n^3 x}{e}-\frac {1191 b^3 g m n^3 x}{j}-\frac {3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac {3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac {6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {3 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac {3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac {3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac {3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac {3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac {1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac {9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac {3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac {9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac {3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}-\frac {472827 b^3 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {(3 b g m n) \int (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{4 e}-\frac {(3 b d g m n) \int \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \, dx}{4 e}-\frac {\left (3 b d^2 g j m n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{\frac {397 e-d j}{e}+\frac {j x}{e}} \, dx,x,d+e x\right )}{4 e^3}-\frac {\left (3 b d^2 g j m n\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right )^2}{\frac {397 e-d j}{e}+\frac {j x}{e}} \, dx,x,d+e x\right )}{2 e^3}+\frac {\left (3 b^2 d g m n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{e^2}-\frac {\left (472827 b^2 g m n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (\frac {e \left (\frac {397 e-d j}{e}+\frac {j x}{e}\right )}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 j^2}+\frac {\left (1191 b^2 g m n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{2 e j}-\frac {\left (1191 b^2 d g m n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (\frac {e \left (\frac {397 e-d j}{e}+\frac {j x}{e}\right )}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e j}-\frac {1}{4} \left (3 b^2 g j m n^2\right ) \int \left (-\frac {397 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^2}+\frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )}{j}+\frac {157609 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^2 (397+j x)}\right ) \, dx+\frac {\left (3 b^2 d g j m n^2\right ) \int \left (\frac {a+b \log \left (c (d+e x)^n\right )}{j}-\frac {397 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j (397+j x)}\right ) \, dx}{2 e}+\frac {\left (3 b^2 d g j m n^2\right ) \int \left (\frac {a+b \log \left (c (d+e x)^n\right )}{j}-\frac {397 \left (a+b \log \left (c (d+e x)^n\right )\right )}{j (397+j x)}\right ) \, dx}{e}+\frac {1}{2} \left (3 b^3 d g n^3\right ) \int \left (\frac {\log \left (h (397+j x)^m\right )}{e}-\frac {d \log \left (h (397+j x)^m\right )}{e (d+e x)}\right ) \, dx+\left (3 b^3 d g n^3\right ) \int \left (\frac {\log \left (h (397+j x)^m\right )}{e}-\frac {d \log \left (h (397+j x)^m\right )}{e (d+e x)}\right ) \, dx-\frac {1}{4} \left (3 b^3 e g n^3\right ) \int \left (-\frac {d \log \left (h (397+j x)^m\right )}{e^2}+\frac {x \log \left (h (397+j x)^m\right )}{e}+\frac {d^2 \log \left (h (397+j x)^m\right )}{e^2 (d+e x)}\right ) \, dx+\frac {\left (3 b^3 d^2 g m n^3\right ) \text {Subst}\left (\int \frac {\text {Li}_3\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}\\ &=-\frac {6 a b^2 d f n^2 x}{e}+\frac {6 a b^2 d g m n^2 x}{e}+\frac {3573 a b^2 g m n^2 x}{2 j}+\frac {6 b^3 d f n^3 x}{e}-\frac {3 b^3 d g m n^3 x}{e}-\frac {1191 b^3 g m n^3 x}{j}-\frac {3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac {3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac {6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {3 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {1191 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}+\frac {3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac {3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {3 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac {3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac {3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{8 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac {1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac {9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac {3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac {9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e j}+\frac {3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {3 b^3 d^2 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}-\frac {472827 b^3 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {(3 b g m n) \text {Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e^2}-\frac {(3 b d g m n) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right )^2 \, dx,x,d+e x\right )}{4 e^2}-\frac {1}{4} \left (3 b^2 g m n^2\right ) \int x \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx+\frac {\left (3 b^3 d g m n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac {\left (3 b^2 d^2 g m n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac {\left (3 b^2 d^2 g m n^2\right ) \text {Subst}\left (\int \frac {\left (a+b \log \left (c x^n\right )\right ) \log \left (1+\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}+\frac {\left (3 b^2 d g m n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{2 e}+\frac {\left (3 b^2 d g m n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{e}-\frac {\left (1191 b^2 d g m n^2\right ) \int \frac {a+b \log \left (c (d+e x)^n\right )}{397+j x} \, dx}{2 e}-\frac {\left (1191 b^2 d g m n^2\right ) \int \frac {a+b \log \left (c (d+e x)^n\right )}{397+j x} \, dx}{e}+\frac {\left (1191 b^2 g m n^2\right ) \int \left (a+b \log \left (c (d+e x)^n\right )\right ) \, dx}{4 j}-\frac {\left (472827 b^2 g m n^2\right ) \int \frac {a+b \log \left (c (d+e x)^n\right )}{397+j x} \, dx}{4 j}+\frac {\left (1191 b^3 g m n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{2 e j}-\frac {1}{4} \left (3 b^3 g n^3\right ) \int x \log \left (h (397+j x)^m\right ) \, dx+\frac {\left (3 b^3 d g n^3\right ) \int \log \left (h (397+j x)^m\right ) \, dx}{4 e}+\frac {\left (3 b^3 d g n^3\right ) \int \log \left (h (397+j x)^m\right ) \, dx}{2 e}+\frac {\left (3 b^3 d g n^3\right ) \int \log \left (h (397+j x)^m\right ) \, dx}{e}-\frac {\left (3 b^3 d^2 g n^3\right ) \int \frac {\log \left (h (397+j x)^m\right )}{d+e x} \, dx}{4 e}-\frac {\left (3 b^3 d^2 g n^3\right ) \int \frac {\log \left (h (397+j x)^m\right )}{d+e x} \, dx}{2 e}-\frac {\left (3 b^3 d^2 g n^3\right ) \int \frac {\log \left (h (397+j x)^m\right )}{d+e x} \, dx}{e}-\frac {\left (472827 b^3 g m n^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 j^2}-\frac {\left (1191 b^3 d g m n^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e j}\\ &=-\frac {6 a b^2 d f n^2 x}{e}+\frac {21 a b^2 d g m n^2 x}{2 e}+\frac {8337 a b^2 g m n^2 x}{4 j}+\frac {6 b^3 d f n^3 x}{e}-\frac {6 b^3 d g m n^3 x}{e}-\frac {3573 b^3 g m n^3 x}{2 j}-\frac {3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac {3 b^3 g m n^3 (d+e x)^2}{16 e^2}-\frac {6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {6 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {3573 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{2 e j}-\frac {3}{8} b^2 g m n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac {3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac {3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{8 e^2}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {15 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac {3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac {3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac {3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}-\frac {3573 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}+\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac {1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac {3}{8} b^3 g n^3 x^2 \log \left (h (397+j x)^m\right )-\frac {21 b^3 d^2 g n^3 \log \left (-\frac {j (d+e x)}{397 e-d j}\right ) \log \left (h (397+j x)^m\right )}{4 e^2}-\frac {9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac {3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac {9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {9 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e j}+\frac {3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {472827 b^3 g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {1191 b^3 d g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e j}-\frac {3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {3 b^3 d^2 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}-\frac {472827 b^3 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}-\frac {\left (3 b^2 g m n^2\right ) \text {Subst}\left (\int x \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{4 e^2}+\frac {\left (3 b^2 d g m n^2\right ) \text {Subst}\left (\int \left (a+b \log \left (c x^n\right )\right ) \, dx,x,d+e x\right )}{2 e^2}+\frac {\left (3 b^3 d g m n^2\right ) \int \log \left (c (d+e x)^n\right ) \, dx}{2 e}+\frac {\left (3 b^3 d g m n^2\right ) \int \log \left (c (d+e x)^n\right ) \, dx}{e}+\frac {\left (1191 b^3 g m n^2\right ) \int \log \left (c (d+e x)^n\right ) \, dx}{4 j}+\frac {\left (3 b^3 d g n^3\right ) \text {Subst}\left (\int \log \left (h x^m\right ) \, dx,x,397+j x\right )}{4 e j}+\frac {\left (3 b^3 d g n^3\right ) \text {Subst}\left (\int \log \left (h x^m\right ) \, dx,x,397+j x\right )}{2 e j}+\frac {\left (3 b^3 d g n^3\right ) \text {Subst}\left (\int \log \left (h x^m\right ) \, dx,x,397+j x\right )}{e j}+\frac {\left (3 b^3 d^2 g m n^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e^2}+\frac {\left (3 b^3 d^2 g m n^3\right ) \text {Subst}\left (\int \frac {\text {Li}_2\left (-\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e^2}+\frac {1}{8} \left (3 b^3 e g m n^3\right ) \int \frac {x^2}{d+e x} \, dx+\frac {\left (472827 b^3 e g m n^3\right ) \int \frac {\log \left (\frac {e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{4 j^2}+\frac {\left (1191 b^3 d g m n^3\right ) \int \frac {\log \left (\frac {e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{2 j}+\frac {\left (1191 b^3 d g m n^3\right ) \int \frac {\log \left (\frac {e (397+j x)}{397 e-d j}\right )}{d+e x} \, dx}{j}+\frac {1}{8} \left (3 b^3 g j m n^3\right ) \int \frac {x^2}{397+j x} \, dx+\frac {\left (3 b^3 d^2 g j m n^3\right ) \int \frac {\log \left (\frac {j (d+e x)}{-397 e+d j}\right )}{397+j x} \, dx}{4 e^2}+\frac {\left (3 b^3 d^2 g j m n^3\right ) \int \frac {\log \left (\frac {j (d+e x)}{-397 e+d j}\right )}{397+j x} \, dx}{2 e^2}+\frac {\left (3 b^3 d^2 g j m n^3\right ) \int \frac {\log \left (\frac {j (d+e x)}{-397 e+d j}\right )}{397+j x} \, dx}{e^2}\\ &=-\frac {6 a b^2 d f n^2 x}{e}+\frac {12 a b^2 d g m n^2 x}{e}+\frac {8337 a b^2 g m n^2 x}{4 j}+\frac {6 b^3 d f n^3 x}{e}-\frac {45 b^3 d g m n^3 x}{4 e}-\frac {3573 b^3 g m n^3 x}{2 j}-\frac {3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac {3 b^3 g m n^3 (d+e x)^2}{8 e^2}-\frac {6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {6 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {3573 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{2 e j}-\frac {3}{8} b^2 g m n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac {3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac {3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {15 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac {3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac {3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac {3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}-\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}-\frac {3573 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}+\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac {1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac {3}{8} b^3 g n^3 x^2 \log \left (h (397+j x)^m\right )+\frac {21 b^3 d g n^3 (397+j x) \log \left (h (397+j x)^m\right )}{4 e j}-\frac {21 b^3 d^2 g n^3 \log \left (-\frac {j (d+e x)}{397 e-d j}\right ) \log \left (h (397+j x)^m\right )}{4 e^2}-\frac {9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac {3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac {9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {9 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e j}+\frac {3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {9 b^3 d^2 g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b^3 g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {1191 b^3 d g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e j}-\frac {3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {3 b^3 d^2 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}-\frac {472827 b^3 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+2 \frac {\left (3 b^3 d g m n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{2 e^2}+\frac {\left (3 b^3 d g m n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{e^2}+\frac {\left (1191 b^3 g m n^2\right ) \text {Subst}\left (\int \log \left (c x^n\right ) \, dx,x,d+e x\right )}{4 e j}+\frac {\left (3 b^3 d^2 g m n^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {e x}{-397 e+d j}\right )}{x} \, dx,x,397+j x\right )}{4 e^2}+\frac {\left (3 b^3 d^2 g m n^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {e x}{-397 e+d j}\right )}{x} \, dx,x,397+j x\right )}{2 e^2}+\frac {\left (3 b^3 d^2 g m n^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {e x}{-397 e+d j}\right )}{x} \, dx,x,397+j x\right )}{e^2}+\frac {1}{8} \left (3 b^3 e g m n^3\right ) \int \left (-\frac {d}{e^2}+\frac {x}{e}+\frac {d^2}{e^2 (d+e x)}\right ) \, dx+\frac {\left (472827 b^3 g m n^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{4 j^2}+\frac {\left (1191 b^3 d g m n^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{2 e j}+\frac {\left (1191 b^3 d g m n^3\right ) \text {Subst}\left (\int \frac {\log \left (1+\frac {j x}{397 e-d j}\right )}{x} \, dx,x,d+e x\right )}{e j}+\frac {1}{8} \left (3 b^3 g j m n^3\right ) \int \left (-\frac {397}{j^2}+\frac {x}{j}+\frac {157609}{j^2 (397+j x)}\right ) \, dx\\ &=-\frac {6 a b^2 d f n^2 x}{e}+\frac {12 a b^2 d g m n^2 x}{e}+\frac {8337 a b^2 g m n^2 x}{4 j}+\frac {6 b^3 d f n^3 x}{e}-\frac {117 b^3 d g m n^3 x}{8 e}-\frac {17865 b^3 g m n^3 x}{8 j}+\frac {3}{8} b^3 g m n^3 x^2-\frac {3 b^3 f n^3 (d+e x)^2}{8 e^2}+\frac {3 b^3 g m n^3 (d+e x)^2}{8 e^2}+\frac {3 b^3 d^2 g m n^3 \log (d+e x)}{8 e^2}-\frac {6 b^3 d f n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {9 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {8337 b^3 g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{4 e j}-\frac {3}{8} b^2 g m n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )+\frac {3 b^2 f n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}-\frac {3 b^2 g m n^2 (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )}{4 e^2}+\frac {3 b d f n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {15 b d g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac {3573 b g m n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e j}-\frac {3 b f n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}+\frac {3 b g m n (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{4 e^2}-\frac {d^2 f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {d g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e^2}+\frac {397 g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{2 e j}-\frac {g m (d+e x)^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{4 e^2}+2 \left (-\frac {3 b^3 d g m n^3 x}{2 e}+\frac {3 b^3 d g m n^2 (d+e x) \log \left (c (d+e x)^n\right )}{2 e^2}\right )+\frac {472827 b^3 g m n^3 \log (397+j x)}{8 j^2}-\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}-\frac {3573 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}+\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{4 j^2}+\frac {1191 b d g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 e j}-\frac {157609 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (\frac {e (397+j x)}{397 e-d j}\right )}{2 j^2}-\frac {3}{8} b^3 g n^3 x^2 \log \left (h (397+j x)^m\right )+\frac {21 b^3 d g n^3 (397+j x) \log \left (h (397+j x)^m\right )}{4 e j}-\frac {21 b^3 d^2 g n^3 \log \left (-\frac {j (d+e x)}{397 e-d j}\right ) \log \left (h (397+j x)^m\right )}{4 e^2}-\frac {9 b^2 d g n^2 x \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )}{2 e}+\frac {3}{4} b^2 g n^2 x^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \log \left (h (397+j x)^m\right )+\frac {9 b d^2 g n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{4 e^2}+\frac {3 b d g n x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )}{2 e}-\frac {3}{4} b g n x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (h (397+j x)^m\right )-\frac {d^2 g \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (h (397+j x)^m\right )}{2 e^2}+\frac {1}{2} x^2 \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (397+j x)^m\right )\right )-\frac {9 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{4 e^2}+\frac {d^2 g m \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \log \left (1+\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b^3 g m n^3 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{4 j^2}-\frac {3573 b^3 d g m n^3 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e j}-\frac {9 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}+\frac {1191 b^2 d g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e j}+\frac {3 b d^2 g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b g m n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \text {Li}_2\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {21 b^3 d^2 g m n^3 \text {Li}_2\left (\frac {e (397+j x)}{397 e-d j}\right )}{4 e^2}+\frac {9 b^3 d^2 g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 e^2}-\frac {472827 b^3 g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{2 j^2}-\frac {1191 b^3 d g m n^3 \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e j}-\frac {3 b^2 d^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}+\frac {472827 b^2 g m n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \text {Li}_3\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}+\frac {3 b^3 d^2 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{e^2}-\frac {472827 b^3 g m n^3 \text {Li}_4\left (-\frac {j (d+e x)}{397 e-d j}\right )}{j^2}\\ \end {align*}

________________________________________________________________________________________

Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(4971\) vs. \(2(2050)=4100\).
time = 2.07, size = 4971, normalized size = 2.42 \begin {gather*} \text {Result too large to show} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]),x]

[Out]

(-12*a^2*b*d*e*g*i*j*m*n + 12*a*b^2*d*e*g*i*j*m*n^2 + 24*a*b^2*d^2*g*j^2*m*n^2 - 6*b^3*d*e*g*i*j*m*n^3 - 36*b^
3*d^2*g*j^2*m*n^3 + 4*a^3*e^2*g*i*j*m*x + 12*a^2*b*d*e*f*j^2*n*x - 18*a^2*b*e^2*g*i*j*m*n*x - 18*a^2*b*d*e*g*j
^2*m*n*x - 36*a*b^2*d*e*f*j^2*n^2*x + 42*a*b^2*e^2*g*i*j*m*n^2*x + 84*a*b^2*d*e*g*j^2*m*n^2*x + 42*b^3*d*e*f*j
^2*n^3*x - 45*b^3*e^2*g*i*j*m*n^3*x - 135*b^3*d*e*g*j^2*m*n^3*x + 4*a^3*e^2*f*j^2*x^2 - 2*a^3*e^2*g*j^2*m*x^2
- 6*a^2*b*e^2*f*j^2*n*x^2 + 6*a^2*b*e^2*g*j^2*m*n*x^2 + 6*a*b^2*e^2*f*j^2*n^2*x^2 - 9*a*b^2*e^2*g*j^2*m*n^2*x^
2 - 3*b^3*e^2*f*j^2*n^3*x^2 + 6*b^3*e^2*g*j^2*m*n^3*x^2 - 12*a^2*b*d^2*f*j^2*n*Log[d + e*x] + 12*a^2*b*d*e*g*i
*j*m*n*Log[d + e*x] + 6*a^2*b*d^2*g*j^2*m*n*Log[d + e*x] + 36*a*b^2*d^2*f*j^2*n^2*Log[d + e*x] - 12*a*b^2*d*e*
g*i*j*m*n^2*Log[d + e*x] - 48*a*b^2*d^2*g*j^2*m*n^2*Log[d + e*x] - 42*b^3*d^2*f*j^2*n^3*Log[d + e*x] + 30*b^3*
d*e*g*i*j*m*n^3*Log[d + e*x] + 69*b^3*d^2*g*j^2*m*n^3*Log[d + e*x] + 12*a*b^2*d^2*f*j^2*n^2*Log[d + e*x]^2 - 1
2*a*b^2*d*e*g*i*j*m*n^2*Log[d + e*x]^2 - 6*a*b^2*d^2*g*j^2*m*n^2*Log[d + e*x]^2 - 18*b^3*d^2*f*j^2*n^3*Log[d +
e*x]^2 + 6*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]^2 + 24*b^3*d^2*g*j^2*m*n^3*Log[d + e*x]^2 - 4*b^3*d^2*f*j^2*n^3*L
og[d + e*x]^3 + 4*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]^3 + 2*b^3*d^2*g*j^2*m*n^3*Log[d + e*x]^3 - 24*a*b^2*d*e*g*i
*j*m*n*Log[c*(d + e*x)^n] + 12*b^3*d*e*g*i*j*m*n^2*Log[c*(d + e*x)^n] + 24*b^3*d^2*g*j^2*m*n^2*Log[c*(d + e*x)
^n] + 12*a^2*b*e^2*g*i*j*m*x*Log[c*(d + e*x)^n] + 24*a*b^2*d*e*f*j^2*n*x*Log[c*(d + e*x)^n] - 36*a*b^2*e^2*g*i
*j*m*n*x*Log[c*(d + e*x)^n] - 36*a*b^2*d*e*g*j^2*m*n*x*Log[c*(d + e*x)^n] - 36*b^3*d*e*f*j^2*n^2*x*Log[c*(d +
e*x)^n] + 42*b^3*e^2*g*i*j*m*n^2*x*Log[c*(d + e*x)^n] + 84*b^3*d*e*g*j^2*m*n^2*x*Log[c*(d + e*x)^n] + 12*a^2*b
*e^2*f*j^2*x^2*Log[c*(d + e*x)^n] - 6*a^2*b*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n] - 12*a*b^2*e^2*f*j^2*n*x^2*Log[
c*(d + e*x)^n] + 12*a*b^2*e^2*g*j^2*m*n*x^2*Log[c*(d + e*x)^n] + 6*b^3*e^2*f*j^2*n^2*x^2*Log[c*(d + e*x)^n] -
9*b^3*e^2*g*j^2*m*n^2*x^2*Log[c*(d + e*x)^n] - 24*a*b^2*d^2*f*j^2*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 24*a*b^2
*d*e*g*i*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 12*a*b^2*d^2*g*j^2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 36*b
^3*d^2*f*j^2*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] - 12*b^3*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] - 48
*b^3*d^2*g*j^2*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] + 12*b^3*d^2*f*j^2*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n]
- 12*b^3*d*e*g*i*j*m*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n] - 6*b^3*d^2*g*j^2*m*n^2*Log[d + e*x]^2*Log[c*(d + e
*x)^n] - 12*b^3*d*e*g*i*j*m*n*Log[c*(d + e*x)^n]^2 + 12*a*b^2*e^2*g*i*j*m*x*Log[c*(d + e*x)^n]^2 + 12*b^3*d*e*
f*j^2*n*x*Log[c*(d + e*x)^n]^2 - 18*b^3*e^2*g*i*j*m*n*x*Log[c*(d + e*x)^n]^2 - 18*b^3*d*e*g*j^2*m*n*x*Log[c*(d
+ e*x)^n]^2 + 12*a*b^2*e^2*f*j^2*x^2*Log[c*(d + e*x)^n]^2 - 6*a*b^2*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n]^2 - 6*
b^3*e^2*f*j^2*n*x^2*Log[c*(d + e*x)^n]^2 + 6*b^3*e^2*g*j^2*m*n*x^2*Log[c*(d + e*x)^n]^2 - 12*b^3*d^2*f*j^2*n*L
og[d + e*x]*Log[c*(d + e*x)^n]^2 + 12*b^3*d*e*g*i*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 + 6*b^3*d^2*g*j^2*m*
n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 + 4*b^3*e^2*g*i*j*m*x*Log[c*(d + e*x)^n]^3 + 4*b^3*e^2*f*j^2*x^2*Log[c*(d
+ e*x)^n]^3 - 2*b^3*e^2*g*j^2*m*x^2*Log[c*(d + e*x)^n]^3 - 4*a^3*e^2*g*i^2*m*Log[i + j*x] + 6*a^2*b*e^2*g*i^2*
m*n*Log[i + j*x] + 12*a^2*b*d*e*g*i*j*m*n*Log[i + j*x] - 6*a*b^2*e^2*g*i^2*m*n^2*Log[i + j*x] - 36*a*b^2*d*e*g
*i*j*m*n^2*Log[i + j*x] + 3*b^3*e^2*g*i^2*m*n^3*Log[i + j*x] + 42*b^3*d*e*g*i*j*m*n^3*Log[i + j*x] + 12*a^2*b*
e^2*g*i^2*m*n*Log[d + e*x]*Log[i + j*x] - 12*a*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[i + j*x] - 24*a*b^2*d*e*g*
i*j*m*n^2*Log[d + e*x]*Log[i + j*x] + 6*b^3*e^2*g*i^2*m*n^3*Log[d + e*x]*Log[i + j*x] + 36*b^3*d*e*g*i*j*m*n^3
*Log[d + e*x]*Log[i + j*x] - 12*a*b^2*e^2*g*i^2*m*n^2*Log[d + e*x]^2*Log[i + j*x] + 6*b^3*e^2*g*i^2*m*n^3*Log[
d + e*x]^2*Log[i + j*x] + 12*b^3*d*e*g*i*j*m*n^3*Log[d + e*x]^2*Log[i + j*x] + 4*b^3*e^2*g*i^2*m*n^3*Log[d + e
*x]^3*Log[i + j*x] - 12*a^2*b*e^2*g*i^2*m*Log[c*(d + e*x)^n]*Log[i + j*x] + 12*a*b^2*e^2*g*i^2*m*n*Log[c*(d +
e*x)^n]*Log[i + j*x] + 24*a*b^2*d*e*g*i*j*m*n*Log[c*(d + e*x)^n]*Log[i + j*x] - 6*b^3*e^2*g*i^2*m*n^2*Log[c*(d
+ e*x)^n]*Log[i + j*x] - 36*b^3*d*e*g*i*j*m*n^2*Log[c*(d + e*x)^n]*Log[i + j*x] + 24*a*b^2*e^2*g*i^2*m*n*Log[
d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] - 12*b^3*e^2*g*i^2*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x]
- 24*b^3*d*e*g*i*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n]*Log[i + j*x] - 12*b^3*e^2*g*i^2*m*n^2*Log[d + e*x]^2
*Log[c*(d + e*x)^n]*Log[i + j*x] - 12*a*b^2*e^2*g*i^2*m*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 6*b^3*e^2*g*i^2*m*
n*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 12*b^3*d*e*g*i*j*m*n*Log[c*(d + e*x)^n]^2*Log[i + j*x] + 12*b^3*e^2*g*i^
2*m*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2*Log[i + j*x] - 4*b^3*e^2*g*i^2*m*Log[c*(d + e*x)^n]^3*Log[i + j*x] - 1
2*a^2*b*e^2*g*i^2*m*n*Log[d + e*x]*Log[(e*(i + j*x))/(e*i - d*j)] + 12*a^2*b*d^2*g*j^2*m*n*Log[d + e*x]*Log[(e
*(i + j*x))/(e*i - d*j)] + 12*a*b^2*e^2*g*i^2*m...

________________________________________________________________________________________

Maple [F]
time = 0.15, size = 0, normalized size = 0.00 \[\int x \left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )^{3} \left (f +g \ln \left (h \left (j x +i \right )^{m}\right )\right )\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*(a+b*ln(c*(e*x+d)^n))^3*(f+g*ln(h*(j*x+i)^m)),x)

[Out]

int(x*(a+b*ln(c*(e*x+d)^n))^3*(f+g*ln(h*(j*x+i)^m)),x)

________________________________________________________________________________________

Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*log(c*(e*x+d)^n))^3*(f+g*log(h*(j*x+i)^m)),x, algorithm="maxima")

[Out]

1/2*b^3*f*x^2*log((x*e + d)^n*c)^3 + 3/2*a*b^2*f*x^2*log((x*e + d)^n*c)^2 - 1/4*a^3*g*j*m*((j*x^2 - 2*I*x)/j^2
- 2*log(j*x + I)/j^3) - 3/4*(2*d^2*e^(-3)*log(x*e + d) + (x^2*e - 2*d*x)*e^(-2))*a^2*b*f*n*e + 3/2*a^2*b*f*x^
2*log((x*e + d)^n*c) + 1/2*a^3*g*x^2*log((j*x + I)^m*h) + 1/2*a^3*f*x^2 + 3/4*((2*d^2*log(x*e + d)^2 + x^2*e^2
- 6*d*x*e + 6*d^2*log(x*e + d))*n^2*e^(-2) - 2*(2*d^2*e^(-3)*log(x*e + d) + (x^2*e - 2*d*x)*e^(-2))*n*e*log((
x*e + d)^n*c))*a*b^2*f - 1/8*(6*(2*d^2*e^(-3)*log(x*e + d) + (x^2*e - 2*d*x)*e^(-2))*n*e*log((x*e + d)^n*c)^2
+ ((4*d^2*log(x*e + d)^3 + 18*d^2*log(x*e + d)^2 + 3*x^2*e^2 - 42*d*x*e + 42*d^2*log(x*e + d))*n^2*e^(-3) - 6*
(2*d^2*log(x*e + d)^2 + x^2*e^2 - 6*d*x*e + 6*d^2*log(x*e + d))*n*e^(-3)*log((x*e + d)^n*c))*n*e)*b^3*f - 1/8*
(2*(-2*I*b^3*g*j*m*x*e^2 + (j^2*m - 2*j^2*log(h))*b^3*g*x^2*e^2 - 2*b^3*g*m*e^2*log(j*x + I))*log((x*e + d)^n)
^3 + (4*b^3*d^2*g*j^2*n^3*log(x*e + d)^3 - 4*b^3*g*j^2*x^2*e^2*log((x*e + d)^n)^3 + (6*(g*j^2*n - 2*g*j^2*log(
c))*a^2*b - 6*(g*j^2*n^2 - 2*g*j^2*n*log(c) + 2*g*j^2*log(c)^2)*a*b^2 + (3*g*j^2*n^3 - 6*g*j^2*n^2*log(c) + 6*
g*j^2*n*log(c)^2 - 4*g*j^2*log(c)^3)*b^3)*x^2*e^2 - 6*(2*a^2*b*d*g*j^2*n - 2*(3*d*g*j^2*n^2 - 2*d*g*j^2*n*log(
c))*a*b^2 + (7*d*g*j^2*n^3 - 6*d*g*j^2*n^2*log(c) + 2*d*g*j^2*n*log(c)^2)*b^3)*x*e - 6*(2*a*b^2*d^2*g*j^2*n^2
- (3*d^2*g*j^2*n^3 - 2*d^2*g*j^2*n^2*log(c))*b^3)*log(x*e + d)^2 - 6*(2*b^3*d*g*j^2*n*x*e - 2*b^3*d^2*g*j^2*n*
log(x*e + d) + (2*a*b^2*g*j^2 - (g*j^2*n - 2*g*j^2*log(c))*b^3)*x^2*e^2)*log((x*e + d)^n)^2 + 6*(2*a^2*b*d^2*g
*j^2*n - 2*(3*d^2*g*j^2*n^2 - 2*d^2*g*j^2*n*log(c))*a*b^2 + (7*d^2*g*j^2*n^3 - 6*d^2*g*j^2*n^2*log(c) + 2*d^2*
g*j^2*n*log(c)^2)*b^3)*log(x*e + d) - 6*(2*b^3*d^2*g*j^2*n^2*log(x*e + d)^2 + (2*a^2*b*g*j^2 - 2*(g*j^2*n - 2*
g*j^2*log(c))*a*b^2 + (g*j^2*n^2 - 2*g*j^2*n*log(c) + 2*g*j^2*log(c)^2)*b^3)*x^2*e^2 + 2*(2*a*b^2*d*g*j^2*n -
(3*d*g*j^2*n^2 - 2*d*g*j^2*n*log(c))*b^3)*x*e - 2*(2*a*b^2*d^2*g*j^2*n - (3*d^2*g*j^2*n^2 - 2*d^2*g*j^2*n*log(
c))*b^3)*log(x*e + d))*log((x*e + d)^n))*log((j*x + I)^m))*e^(-2)/j^2 - integrate(-1/8*((6*(g*j^3*m*n - 2*(j^3
*m - 2*j^3*log(h))*g*log(c))*a^2*b - 6*(g*j^3*m*n^2 - 2*g*j^3*m*n*log(c) + 2*(j^3*m - 2*j^3*log(h))*g*log(c)^2
)*a*b^2 + (3*g*j^3*m*n^3 - 6*g*j^3*m*n^2*log(c) + 6*g*j^3*m*n*log(c)^2 - 4*(j^3*m - 2*j^3*log(h))*g*log(c)^3)*
b^3)*x^3*e^3 + 4*(b^3*d^2*g*j^3*m*n^3*x*e + b^3*d^3*g*j^3*m*n^3)*log(x*e + d)^3 + (8*(I*b^3*g*j^2*log(c)^3*log
(h) + 3*I*a*b^2*g*j^2*log(c)^2*log(h) + 3*I*a^2*b*g*j^2*log(c)*log(h))*e^3 - (6*(d*g*j^3*m*n + 2*(j^3*m - 2*j^
3*log(h))*d*g*log(c))*a^2*b - 6*(5*d*g*j^3*m*n^2 - 2*d*g*j^3*m*n*log(c) - 2*(j^3*m - 2*j^3*log(h))*d*g*log(c)^
2)*a*b^2 + (39*d*g*j^3*m*n^3 - 30*d*g*j^3*m*n^2*log(c) + 6*d*g*j^3*m*n*log(c)^2 + 4*(j^3*m - 2*j^3*log(h))*d*g
*log(c)^3)*b^3)*e^2)*x^2 - 6*(2*a*b^2*d^3*g*j^3*m*n^2 - (3*d^3*g*j^3*m*n^3 - 2*d^3*g*j^3*m*n^2*log(c))*b^3 + (
2*a*b^2*d^2*g*j^3*m*n^2 - (3*d^2*g*j^3*m*n^3 - 2*d^2*g*j^3*m*n^2*log(c))*b^3)*x*e)*log(x*e + d)^2 - 6*(2*((j^3
*m - 2*j^3*log(h))*a*b^2*g + ((j^3*m - 2*j^3*log(h))*g*log(c) - (j^3*m*n - j^3*n*log(h))*g)*b^3)*x^3*e^3 - ((4
*I*a*b^2*g*j^2*log(h) + (4*I*g*j^2*log(c)*log(h) + (-I*j^2*m*n - 2*I*j^2*n*log(h))*g)*b^3)*e^3 - (2*(j^3*m - 2
*j^3*log(h))*a*b^2*d*g + (d*g*j^3*m*n + 2*(j^3*m - 2*j^3*log(h))*d*g*log(c))*b^3)*e^2)*x^2 + 2*(b^3*d^2*g*j^3*
m*n*e - b^3*g*j*m*n*e^3 - 2*(I*b^3*d*g*j^2*log(c)*log(h) + I*a*b^2*d*g*j^2*log(h))*e^2)*x + 2*(b^3*g*j*m*n*x*e
^3 + I*b^3*g*m*n*e^3)*log(j*x + I) - 2*(b^3*d^2*g*j^3*m*n*x*e + b^3*d^3*g*j^3*m*n)*log(x*e + d))*log((x*e + d)
^n)^2 + 2*(4*(I*b^3*d*g*j^2*log(c)^3*log(h) + 3*I*a*b^2*d*g*j^2*log(c)^2*log(h) + 3*I*a^2*b*d*g*j^2*log(c)*log
(h))*e^2 - 3*(2*a^2*b*d^2*g*j^3*m*n - 2*(3*d^2*g*j^3*m*n^2 - 2*d^2*g*j^3*m*n*log(c))*a*b^2 + (7*d^2*g*j^3*m*n^
3 - 6*d^2*g*j^3*m*n^2*log(c) + 2*d^2*g*j^3*m*n*log(c)^2)*b^3)*e)*x + 6*(2*a^2*b*d^3*g*j^3*m*n - 2*(3*d^3*g*j^3
*m*n^2 - 2*d^3*g*j^3*m*n*log(c))*a*b^2 + (7*d^3*g*j^3*m*n^3 - 6*d^3*g*j^3*m*n^2*log(c) + 2*d^3*g*j^3*m*n*log(c
)^2)*b^3 + (2*a^2*b*d^2*g*j^3*m*n - 2*(3*d^2*g*j^3*m*n^2 - 2*d^2*g*j^3*m*n*log(c))*a*b^2 + (7*d^2*g*j^3*m*n^3
- 6*d^2*g*j^3*m*n^2*log(c) + 2*d^2*g*j^3*m*n*log(c)^2)*b^3)*x*e)*log(x*e + d) - 6*((2*(j^3*m - 2*j^3*log(h))*a
^2*b*g - 2*(g*j^3*m*n - 2*(j^3*m - 2*j^3*log(h))*g*log(c))*a*b^2 + (g*j^3*m*n^2 - 2*g*j^3*m*n*log(c) + 2*(j^3*
m - 2*j^3*log(h))*g*log(c)^2)*b^3)*x^3*e^3 - (4*(I*b^3*g*j^2*log(c)^2*log(h) + 2*I*a*b^2*g*j^2*log(c)*log(h) +
I*a^2*b*g*j^2*log(h))*e^3 - (2*(j^3*m - 2*j^3*log(h))*a^2*b*d*g + 2*(d*g*j^3*m*n + 2*(j^3*m - 2*j^3*log(h))*d
*g*log(c))*a*b^2 - (5*d*g*j^3*m*n^2 - 2*d*g*j^3*m*n*log(c) - 2*(j^3*m - 2*j^3*log(h))*d*g*log(c)^2)*b^3)*e^2)*
x^2 + 2*(b^3*d^2*g*j^3*m*n^2*x*e + b^3*d^3*g*j^3*m*n^2)*log(x*e + d)^2 - 2*(2*(I*b^3*d*g*j^2*log(c)^2*log(h) +
2*I*a*b^2*d*g*j^2*log(c)*log(h) + I*a^2*b*d*g*j^2*log(h))*e^2 - (2*a*b^2*d^2*g*j^3*m*n - (3*d^2*g*j^3*m*n^2 -
2*d^2*g*j^3*m*n*log(c))*b^3)*e)*x - 2*(2*a*b^2*d^3*g*j^3*m*n - (3*d^3*g*j^3*m*n^2 - 2*d^3*g*j^3*m*n*log(c))*b
^3 + (2*a*b^2*d^2*g*j^3*m*n - (3*d^2*g*j^3*m*n^...

________________________________________________________________________________________

Fricas [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*log(c*(e*x+d)^n))^3*(f+g*log(h*(j*x+i)^m)),x, algorithm="fricas")

[Out]

1/4*((2*b^3*g*j^2*n^3*x^2*log(h) + 2*I*b^3*g*j*m*n^3*x - (b^3*g*j^2*m - 2*b^3*f*j^2)*n^3*x^2 + 2*(b^3*g*j^2*m*
n^3*x^2 + b^3*g*m*n^3)*log(j*x + I))*log(x*e + d)^3 + 4*j^2*integral(1/4*(4*a^3*f*j^2*x^2*e + 4*a^3*d*f*j^2*x
+ 4*(b^3*f*j^2*x^2*e + b^3*d*f*j^2*x)*log(c)^3 + 3*(4*a*b^2*d*f*j^2*n^2*x - (2*I*b^3*g*j*m*n^3*x - (4*a*b^2*f*
j^2*n^2 + (b^3*g*j^2*m - 2*b^3*f*j^2)*n^3)*x^2)*e + 2*(2*a*b^2*d*g*j^2*m*n^2*x - (b^3*g*m*n^3 + (b^3*g*j^2*m*n
^3 - 2*a*b^2*g*j^2*m*n^2)*x^2)*e + 2*(b^3*g*j^2*m*n^2*x^2*e + b^3*d*g*j^2*m*n^2*x)*log(c))*log(j*x + I) + 4*(b
^3*f*j^2*n^2*x^2*e + b^3*d*f*j^2*n^2*x)*log(c) + 2*(2*a*b^2*d*g*j^2*n^2*x - (b^3*g*j^2*n^3 - 2*a*b^2*g*j^2*n^2
)*x^2*e + 2*(b^3*g*j^2*n^2*x^2*e + b^3*d*g*j^2*n^2*x)*log(c))*log(h))*log(x*e + d)^2 + 12*(a*b^2*f*j^2*x^2*e +
a*b^2*d*f*j^2*x)*log(c)^2 + 4*(a^3*g*j^2*m*x^2*e + a^3*d*g*j^2*m*x + (b^3*g*j^2*m*x^2*e + b^3*d*g*j^2*m*x)*lo
g(c)^3 + 3*(a*b^2*g*j^2*m*x^2*e + a*b^2*d*g*j^2*m*x)*log(c)^2 + 3*(a^2*b*g*j^2*m*x^2*e + a^2*b*d*g*j^2*m*x)*lo
g(c))*log(j*x + I) + 12*(a^2*b*f*j^2*n*x^2*e + a^2*b*d*f*j^2*n*x + (b^3*f*j^2*n*x^2*e + b^3*d*f*j^2*n*x)*log(c
)^2 + (a^2*b*g*j^2*m*n*x^2*e + a^2*b*d*g*j^2*m*n*x + (b^3*g*j^2*m*n*x^2*e + b^3*d*g*j^2*m*n*x)*log(c)^2 + 2*(a
*b^2*g*j^2*m*n*x^2*e + a*b^2*d*g*j^2*m*n*x)*log(c))*log(j*x + I) + 2*(a*b^2*f*j^2*n*x^2*e + a*b^2*d*f*j^2*n*x)
*log(c) + (a^2*b*g*j^2*n*x^2*e + a^2*b*d*g*j^2*n*x + (b^3*g*j^2*n*x^2*e + b^3*d*g*j^2*n*x)*log(c)^2 + 2*(a*b^2
*g*j^2*n*x^2*e + a*b^2*d*g*j^2*n*x)*log(c))*log(h))*log(x*e + d) + 12*(a^2*b*f*j^2*x^2*e + a^2*b*d*f*j^2*x)*lo
g(c) + 4*(a^3*g*j^2*x^2*e + a^3*d*g*j^2*x + (b^3*g*j^2*x^2*e + b^3*d*g*j^2*x)*log(c)^3 + 3*(a*b^2*g*j^2*x^2*e
+ a*b^2*d*g*j^2*x)*log(c)^2 + 3*(a^2*b*g*j^2*x^2*e + a^2*b*d*g*j^2*x)*log(c))*log(h))/(j^2*x*e + d*j^2), x))/j
^2

________________________________________________________________________________________

Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*ln(c*(e*x+d)**n))**3*(f+g*ln(h*(j*x+i)**m)),x)

[Out]

Timed out

________________________________________________________________________________________

Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x*(a+b*log(c*(e*x+d)^n))^3*(f+g*log(h*(j*x+i)^m)),x, algorithm="giac")

[Out]

integrate((b*log((x*e + d)^n*c) + a)^3*(g*log((j*x + I)^m*h) + f)*x, x)

________________________________________________________________________________________

Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int x\,{\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^3\,\left (f+g\,\ln \left (h\,{\left (i+j\,x\right )}^m\right )\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*(a + b*log(c*(d + e*x)^n))^3*(f + g*log(h*(i + j*x)^m)),x)

[Out]

int(x*(a + b*log(c*(d + e*x)^n))^3*(f + g*log(h*(i + j*x)^m)), x)

________________________________________________________________________________________