Integrand size = 31, antiderivative size = 1147 \[ \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx =\text {Too large to display} \]
-g*m*(e*x+d)*(a+b*ln(c*(e*x+d)^n))^3/e+d*g*(a+b*ln(c*(e*x+d)^n))^3*ln(h*(j *x+i)^m)/e-d*g*m*(a+b*ln(c*(e*x+d)^n))^3*ln(e*(j*x+i)/(-d*j+e*i))/e+g*i*m* (a+b*ln(c*(e*x+d)^n))^3*ln(e*(j*x+i)/(-d*j+e*i))/j-18*a*b^2*g*m*n^2*x+6*b^ 3*f*n^2*(e*x+d)*ln(c*(e*x+d)^n)/e-3*b*f*n*(e*x+d)*(a+b*ln(c*(e*x+d)^n))^2/ e-6*b^3*g*n^3*(j*x+i)*ln(h*(j*x+i)^m)/j+6*b^2*g*n^2*x*(a+b*ln(c*(e*x+d)^n) )*ln(h*(j*x+i)^m)-3*b*g*n*x*(a+b*ln(c*(e*x+d)^n))^2*ln(h*(j*x+i)^m)+6*a*b^ 2*f*n^2*x+24*b^3*g*m*n^3*x-6*b^3*f*n^3*x+6*b^2*g*i*m*n^2*(a+b*ln(c*(e*x+d) ^n))*ln(e*(j*x+i)/(-d*j+e*i))/j+3*b*d*g*m*n*(a+b*ln(c*(e*x+d)^n))^2*ln(e*( j*x+i)/(-d*j+e*i))/e-3*b*g*i*m*n*(a+b*ln(c*(e*x+d)^n))^2*ln(e*(j*x+i)/(-d* j+e*i))/j+6*b^2*d*g*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(2,-j*(e*x+d)/(-d*j +e*i))/e-6*b^2*g*i*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(2,-j*(e*x+d)/(-d*j+ e*i))/j-3*b*d*g*m*n*(a+b*ln(c*(e*x+d)^n))^2*polylog(2,-j*(e*x+d)/(-d*j+e*i ))/e+3*b*g*i*m*n*(a+b*ln(c*(e*x+d)^n))^2*polylog(2,-j*(e*x+d)/(-d*j+e*i))/ j+6*b^2*d*g*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(3,-j*(e*x+d)/(-d*j+e*i))/e -6*b^2*g*i*m*n^2*(a+b*ln(c*(e*x+d)^n))*polylog(3,-j*(e*x+d)/(-d*j+e*i))/j+ 6*b^3*g*i*m*n^3*polylog(2,-j*(e*x+d)/(-d*j+e*i))/j+6*b^3*d*g*m*n^3*polylog (2,e*(j*x+i)/(-d*j+e*i))/e-6*b^3*d*g*m*n^3*polylog(3,-j*(e*x+d)/(-d*j+e*i) )/e+6*b^3*g*i*m*n^3*polylog(3,-j*(e*x+d)/(-d*j+e*i))/j-6*b^3*d*g*m*n^3*pol ylog(4,-j*(e*x+d)/(-d*j+e*i))/e+6*b^3*g*i*m*n^3*polylog(4,-j*(e*x+d)/(-d*j +e*i))/j+6*b^3*d*g*n^3*ln(-j*(e*x+d)/(-d*j+e*i))*ln(h*(j*x+i)^m)/e-3*b*...
Leaf count is larger than twice the leaf count of optimal. \(3163\) vs. \(2(1147)=2294\).
Time = 0.65 (sec) , antiderivative size = 3163, normalized size of antiderivative = 2.76 \[ \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx=\text {Result too large to show} \]
(-3*a^2*b*d*f*j*n + 3*a^2*b*d*g*j*m*n - 6*a*b^2*d*g*j*m*n^2 + 6*b^3*d*g*j* m*n^3 + a^3*e*f*j*x - a^3*e*g*j*m*x - 3*a^2*b*e*f*j*n*x + 6*a^2*b*e*g*j*m* n*x + 6*a*b^2*e*f*j*n^2*x - 18*a*b^2*e*g*j*m*n^2*x - 6*b^3*e*f*j*n^3*x + 2 4*b^3*e*g*j*m*n^3*x + 3*a^2*b*d*f*j*n*Log[d + e*x] - 3*a^2*b*d*g*j*m*n*Log [d + e*x] + 6*a*b^2*d*g*j*m*n^2*Log[d + e*x] + 6*b^3*d*f*j*n^3*Log[d + e*x ] - 12*b^3*d*g*j*m*n^3*Log[d + e*x] - 3*a*b^2*d*f*j*n^2*Log[d + e*x]^2 + 3 *a*b^2*d*g*j*m*n^2*Log[d + e*x]^2 - 3*b^3*d*g*j*m*n^3*Log[d + e*x]^2 + b^3 *d*f*j*n^3*Log[d + e*x]^3 - b^3*d*g*j*m*n^3*Log[d + e*x]^3 - 6*a*b^2*d*f*j *n*Log[c*(d + e*x)^n] + 6*a*b^2*d*g*j*m*n*Log[c*(d + e*x)^n] - 6*b^3*d*g*j *m*n^2*Log[c*(d + e*x)^n] + 3*a^2*b*e*f*j*x*Log[c*(d + e*x)^n] - 3*a^2*b*e *g*j*m*x*Log[c*(d + e*x)^n] - 6*a*b^2*e*f*j*n*x*Log[c*(d + e*x)^n] + 12*a* b^2*e*g*j*m*n*x*Log[c*(d + e*x)^n] + 6*b^3*e*f*j*n^2*x*Log[c*(d + e*x)^n] - 18*b^3*e*g*j*m*n^2*x*Log[c*(d + e*x)^n] + 6*a*b^2*d*f*j*n*Log[d + e*x]*L og[c*(d + e*x)^n] - 6*a*b^2*d*g*j*m*n*Log[d + e*x]*Log[c*(d + e*x)^n] + 6* b^3*d*g*j*m*n^2*Log[d + e*x]*Log[c*(d + e*x)^n] - 3*b^3*d*f*j*n^2*Log[d + e*x]^2*Log[c*(d + e*x)^n] + 3*b^3*d*g*j*m*n^2*Log[d + e*x]^2*Log[c*(d + e* x)^n] - 3*b^3*d*f*j*n*Log[c*(d + e*x)^n]^2 + 3*b^3*d*g*j*m*n*Log[c*(d + e* x)^n]^2 + 3*a*b^2*e*f*j*x*Log[c*(d + e*x)^n]^2 - 3*a*b^2*e*g*j*m*x*Log[c*( d + e*x)^n]^2 - 3*b^3*e*f*j*n*x*Log[c*(d + e*x)^n]^2 + 6*b^3*e*g*j*m*n*x*L og[c*(d + e*x)^n]^2 + 3*b^3*d*f*j*n*Log[d + e*x]*Log[c*(d + e*x)^n]^2 -...
Time = 3.71 (sec) , antiderivative size = 1248, normalized size of antiderivative = 1.09, number of steps used = 5, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.161, Rules used = {2879, 2863, 2009, 7293, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx\) |
| \(\Big \downarrow \) 2879 |
| \(\displaystyle -3 b e n \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{d+e x}dx-g j m \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{i+j x}dx+x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right )\) |
| \(\Big \downarrow \) 2863 |
| \(\displaystyle -3 b e n \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{d+e x}dx-g j m \int \left (\frac {\left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j}-\frac {i \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j (i+j x)}\right )dx+x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right )\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -3 b e n \int \frac {x \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \left (f+g \log \left (h (i+j x)^m\right )\right )}{d+e x}dx-g j m \left (\frac {6 b^2 i n^2 \operatorname {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^2}+\frac {6 a b^2 n^2 x}{j}-\frac {3 b i n \operatorname {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j^2}-\frac {i \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j^2}-\frac {3 b n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e j}+\frac {(d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{e j}+\frac {6 b^3 n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}-\frac {6 b^3 i n^3 \operatorname {PolyLog}\left (4,-\frac {j (d+e x)}{e i-d j}\right )}{j^2}-\frac {6 b^3 n^3 x}{j}\right )+x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right )\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -3 b e n \int \left (\frac {g x \log \left (h (i+j x)^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{d+e x}+\frac {f x \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{d+e x}\right )dx-g j m \left (\frac {6 b^2 i n^2 \operatorname {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{j^2}+\frac {6 a b^2 n^2 x}{j}-\frac {3 b i n \operatorname {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{j^2}-\frac {i \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{j^2}-\frac {3 b n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e j}+\frac {(d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{e j}+\frac {6 b^3 n^2 (d+e x) \log \left (c (d+e x)^n\right )}{e j}-\frac {6 b^3 i n^3 \operatorname {PolyLog}\left (4,-\frac {j (d+e x)}{e i-d j}\right )}{j^2}-\frac {6 b^3 n^3 x}{j}\right )+x \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right )\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle x \left (f+g \log \left (h (i+j x)^m\right )\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^3-3 b e n \left (\frac {d g m \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{3 b e^2 n}-\frac {d g \log \left (h (i+j x)^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{3 b e^2 n}-\frac {d f \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{3 b e^2 n}+\frac {f (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {g m (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {d g m \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}+\frac {g i m \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e j}+\frac {d g \log \left (h (i+j x)^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}+\frac {g x \log \left (h (i+j x)^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e}+\frac {d g m \operatorname {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )^2}{e^2}-\frac {2 b g i m n \log \left (\frac {e (i+j x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{e j}-\frac {2 b g n x \log \left (h (i+j x)^m\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{e}-\frac {2 b d g m n \operatorname {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{e^2}+\frac {2 b g i m n \operatorname {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{e j}-\frac {2 b d g m n \operatorname {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) \left (a+b \log \left (c (d+e x)^n\right )\right )}{e^2}+\frac {2 b^2 f n^2 x}{e}-\frac {6 b^2 g m n^2 x}{e}-\frac {2 a b f n x}{e}+\frac {4 a b g m n x}{e}-\frac {2 b^2 f n (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {4 b^2 g m n (d+e x) \log \left (c (d+e x)^n\right )}{e^2}+\frac {2 b^2 g n^2 (i+j x) \log \left (h (i+j x)^m\right )}{e j}-\frac {2 b^2 d g n^2 \log \left (-\frac {j (d+e x)}{e i-d j}\right ) \log \left (h (i+j x)^m\right )}{e^2}-\frac {2 b^2 g i m n^2 \operatorname {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right )}{e j}-\frac {2 b^2 d g m n^2 \operatorname {PolyLog}\left (2,\frac {e (i+j x)}{e i-d j}\right )}{e^2}+\frac {2 b^2 d g m n^2 \operatorname {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right )}{e^2}-\frac {2 b^2 g i m n^2 \operatorname {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right )}{e j}+\frac {2 b^2 d g m n^2 \operatorname {PolyLog}\left (4,-\frac {j (d+e x)}{e i-d j}\right )}{e^2}\right )-g j m \left (-\frac {6 n^3 x b^3}{j}+\frac {6 n^2 (d+e x) \log \left (c (d+e x)^n\right ) b^3}{e j}-\frac {6 i n^3 \operatorname {PolyLog}\left (4,-\frac {j (d+e x)}{e i-d j}\right ) b^3}{j^2}+\frac {6 a n^2 x b^2}{j}+\frac {6 i n^2 \left (a+b \log \left (c (d+e x)^n\right )\right ) \operatorname {PolyLog}\left (3,-\frac {j (d+e x)}{e i-d j}\right ) b^2}{j^2}-\frac {3 n (d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^2 b}{e j}-\frac {3 i n \left (a+b \log \left (c (d+e x)^n\right )\right )^2 \operatorname {PolyLog}\left (2,-\frac {j (d+e x)}{e i-d j}\right ) b}{j^2}+\frac {(d+e x) \left (a+b \log \left (c (d+e x)^n\right )\right )^3}{e j}-\frac {i \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 )}{j^2}\right )\) |
x*(a + b*Log[c*(d + e*x)^n])^3*(f + g*Log[h*(i + j*x)^m]) - 3*b*e*n*((-2*a *b*f*n*x)/e + (4*a*b*g*m*n*x)/e + (2*b^2*f*n^2*x)/e - (6*b^2*g*m*n^2*x)/e - (2*b^2*f*n*(d + e*x)*Log[c*(d + e*x)^n])/e^2 + (4*b^2*g*m*n*(d + e*x)*Lo g[c*(d + e*x)^n])/e^2 + (f*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^2 - ( g*m*(d + e*x)*(a + b*Log[c*(d + e*x)^n])^2)/e^2 - (d*f*(a + b*Log[c*(d + e *x)^n])^3)/(3*b*e^2*n) - (2*b*g*i*m*n*(a + b*Log[c*(d + e*x)^n])*Log[(e*(i + j*x))/(e*i - d*j)])/(e*j) - (d*g*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e* (i + j*x))/(e*i - d*j)])/e^2 + (g*i*m*(a + b*Log[c*(d + e*x)^n])^2*Log[(e* (i + j*x))/(e*i - d*j)])/(e*j) + (d*g*m*(a + b*Log[c*(d + e*x)^n])^3*Log[( e*(i + j*x))/(e*i - d*j)])/(3*b*e^2*n) + (2*b^2*g*n^2*(i + j*x)*Log[h*(i + j*x)^m])/(e*j) - (2*b^2*d*g*n^2*Log[-((j*(d + e*x))/(e*i - d*j))]*Log[h*( i + j*x)^m])/e^2 - (2*b*g*n*x*(a + b*Log[c*(d + e*x)^n])*Log[h*(i + j*x)^m ])/e + (d*g*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/e^2 + (g*x*(a + b*Log[c*(d + e*x)^n])^2*Log[h*(i + j*x)^m])/e - (d*g*(a + b*Log[c*(d + e*x)^n])^3*Log[h*(i + j*x)^m])/(3*b*e^2*n) - (2*b^2*g*i*m*n^2*PolyLog[2, - ((j*(d + e*x))/(e*i - d*j))])/(e*j) - (2*b*d*g*m*n*(a + b*Log[c*(d + e*x)^ n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/e^2 + (2*b*g*i*m*n*(a + b*Lo g[c*(d + e*x)^n])*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/(e*j) + (d*g*m *(a + b*Log[c*(d + e*x)^n])^2*PolyLog[2, -((j*(d + e*x))/(e*i - d*j))])/e^ 2 - (2*b^2*d*g*m*n^2*PolyLog[2, (e*(i + j*x))/(e*i - d*j)])/e^2 + (2*b^...
3.4.98.3.1 Defintions of rubi rules used
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]
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] + (-Simp[g*j*m Int[x*((a + b*Log[c*(d + e*x)^n])^p/(i + j*x)), x], x] - Simp[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]
\[\int {\left (a +b \ln \left (c \left (e x +d \right )^{n}\right )\right )}^{3} \left (f +g \ln \left (h \left (j x +i \right )^{m}\right )\right )d x\]
\[ \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx=\int { {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{3} {\left (g \log \left ({\left (j x + i\right )}^{m} h\right ) + f\right )} \,d x } \]
integral(b^3*f*log((e*x + d)^n*c)^3 + 3*a*b^2*f*log((e*x + d)^n*c)^2 + 3*a ^2*b*f*log((e*x + d)^n*c) + a^3*f + (b^3*g*log((e*x + d)^n*c)^3 + 3*a*b^2* g*log((e*x + d)^n*c)^2 + 3*a^2*b*g*log((e*x + d)^n*c) + a^3*g)*log((j*x + i)^m*h), x)
Timed out. \[ \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx=\text {Timed out} \]
\[ \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx=\int { {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{3} {\left (g \log \left ({\left (j x + i\right )}^{m} h\right ) + f\right )} \,d x } \]
b^3*f*x*log((e*x + d)^n*c)^3 - 3*a^2*b*e*f*n*(x/e - d*log(e*x + d)/e^2) - a^3*g*j*m*(x/j - i*log(j*x + i)/j^2) + 3*a*b^2*f*x*log((e*x + d)^n*c)^2 + 3*a^2*b*f*x*log((e*x + d)^n*c) + a^3*g*x*log((j*x + i)^m*h) - 3*(2*e*n*(x/ e - d*log(e*x + d)/e^2)*log((e*x + d)^n*c) + (d*log(e*x + d)^2 - 2*e*x + 2 *d*log(e*x + d))*n^2/e)*a*b^2*f - (3*e*n*(x/e - d*log(e*x + d)/e^2)*log((e *x + d)^n*c)^2 - e*n*((d*log(e*x + d)^3 + 3*d*log(e*x + d)^2 - 6*e*x + 6*d *log(e*x + d))*n^2/e^2 - 3*(d*log(e*x + d)^2 - 2*e*x + 2*d*log(e*x + d))*n *log((e*x + d)^n*c)/e^2))*b^3*f + a^3*f*x + ((b^3*e*g*i*m*log(j*x + i) - ( j*m - j*log(h))*b^3*e*g*x)*log((e*x + d)^n)^3 + (b^3*d*g*j*n^3*log(e*x + d )^3 + b^3*e*g*j*x*log((e*x + d)^n)^3 - 3*(a*b^2*d*g*j*n^2 - (d*g*j*n^3 - d *g*j*n^2*log(c))*b^3)*log(e*x + d)^2 + 3*(b^3*d*g*j*n*log(e*x + d) + (a*b^ 2*e*g*j - (e*g*j*n - e*g*j*log(c))*b^3)*x)*log((e*x + d)^n)^2 - (3*(e*g*j* n - e*g*j*log(c))*a^2*b - 3*(2*e*g*j*n^2 - 2*e*g*j*n*log(c) + e*g*j*log(c) ^2)*a*b^2 + (6*e*g*j*n^3 - 6*e*g*j*n^2*log(c) + 3*e*g*j*n*log(c)^2 - e*g*j *log(c)^3)*b^3)*x + 3*(a^2*b*d*g*j*n - 2*(d*g*j*n^2 - d*g*j*n*log(c))*a*b^ 2 + (2*d*g*j*n^3 - 2*d*g*j*n^2*log(c) + d*g*j*n*log(c)^2)*b^3)*log(e*x + d ) - 3*(b^3*d*g*j*n^2*log(e*x + d)^2 - (a^2*b*e*g*j - 2*(e*g*j*n - e*g*j*lo g(c))*a*b^2 + (2*e*g*j*n^2 - 2*e*g*j*n*log(c) + e*g*j*log(c)^2)*b^3)*x - 2 *(a*b^2*d*g*j*n - (d*g*j*n^2 - d*g*j*n*log(c))*b^3)*log(e*x + d))*log((e*x + d)^n))*log((j*x + i)^m))/(e*j) - integrate(-(b^3*d*e*g*i*j*log(c)^3*...
\[ \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx=\int { {\left (b \log \left ({\left (e x + d\right )}^{n} c\right ) + a\right )}^{3} {\left (g \log \left ({\left (j x + i\right )}^{m} h\right ) + f\right )} \,d x } \]
Timed out. \[ \int \left (a+b \log \left (c (d+e x)^n\right )\right )^3 \left (f+g \log \left (h (i+j x)^m\right )\right ) \, dx=\int {\left (a+b\,\ln \left (c\,{\left (d+e\,x\right )}^n\right )\right )}^3\,\left (f+g\,\ln \left (h\,{\left (i+j\,x\right )}^m\right )\right ) \,d x \]