3.65 \(\int \frac {(a+b \log (c x^n))^3 \log (d (\frac {1}{d}+f x^m))}{x} \, dx\)

Optimal. Leaf size=105 \[ -\frac {6 b^2 n^2 \text {Li}_4\left (-d f x^m\right ) \left (a+b \log \left (c x^n\right )\right )}{m^3}+\frac {3 b n \text {Li}_3\left (-d f x^m\right ) \left (a+b \log \left (c x^n\right )\right )^2}{m^2}-\frac {\text {Li}_2\left (-d f x^m\right ) \left (a+b \log \left (c x^n\right )\right )^3}{m}+\frac {6 b^3 n^3 \text {Li}_5\left (-d f x^m\right )}{m^4} \]

[Out]

-(a+b*ln(c*x^n))^3*polylog(2,-d*f*x^m)/m+3*b*n*(a+b*ln(c*x^n))^2*polylog(3,-d*f*x^m)/m^2-6*b^2*n^2*(a+b*ln(c*x
^n))*polylog(4,-d*f*x^m)/m^3+6*b^3*n^3*polylog(5,-d*f*x^m)/m^4

________________________________________________________________________________________

Rubi [A]  time = 0.11, antiderivative size = 105, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.107, Rules used = {2374, 2383, 6589} \[ -\frac {6 b^2 n^2 \text {PolyLog}\left (4,-d f x^m\right ) \left (a+b \log \left (c x^n\right )\right )}{m^3}+\frac {3 b n \text {PolyLog}\left (3,-d f x^m\right ) \left (a+b \log \left (c x^n\right )\right )^2}{m^2}-\frac {\text {PolyLog}\left (2,-d f x^m\right ) \left (a+b \log \left (c x^n\right )\right )^3}{m}+\frac {6 b^3 n^3 \text {PolyLog}\left (5,-d f x^m\right )}{m^4} \]

Antiderivative was successfully verified.

[In]

Int[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^m)])/x,x]

[Out]

-(((a + b*Log[c*x^n])^3*PolyLog[2, -(d*f*x^m)])/m) + (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[3, -(d*f*x^m)])/m^2 -
(6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[4, -(d*f*x^m)])/m^3 + (6*b^3*n^3*PolyLog[5, -(d*f*x^m)])/m^4

Rule 2374

Int[(Log[(d_.)*((e_) + (f_.)*(x_)^(m_.))]*((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.))/(x_), x_Symbol] :> -Sim
p[(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*Log
[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 2383

Int[(((a_.) + Log[(c_.)*(x_)^(n_.)]*(b_.))^(p_.)*PolyLog[k_, (e_.)*(x_)^(q_.)])/(x_), x_Symbol] :> Simp[(PolyL
og[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 6589

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]

Rubi steps

\begin {align*} \int \frac {\left (a+b \log \left (c x^n\right )\right )^3 \log \left (d \left (\frac {1}{d}+f x^m\right )\right )}{x} \, dx &=-\frac {\left (a+b \log \left (c x^n\right )\right )^3 \text {Li}_2\left (-d f x^m\right )}{m}+\frac {(3 b n) \int \frac {\left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_2\left (-d f x^m\right )}{x} \, dx}{m}\\ &=-\frac {\left (a+b \log \left (c x^n\right )\right )^3 \text {Li}_2\left (-d f x^m\right )}{m}+\frac {3 b n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_3\left (-d f x^m\right )}{m^2}-\frac {\left (6 b^2 n^2\right ) \int \frac {\left (a+b \log \left (c x^n\right )\right ) \text {Li}_3\left (-d f x^m\right )}{x} \, dx}{m^2}\\ &=-\frac {\left (a+b \log \left (c x^n\right )\right )^3 \text {Li}_2\left (-d f x^m\right )}{m}+\frac {3 b n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_3\left (-d f x^m\right )}{m^2}-\frac {6 b^2 n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_4\left (-d f x^m\right )}{m^3}+\frac {\left (6 b^3 n^3\right ) \int \frac {\text {Li}_4\left (-d f x^m\right )}{x} \, dx}{m^3}\\ &=-\frac {\left (a+b \log \left (c x^n\right )\right )^3 \text {Li}_2\left (-d f x^m\right )}{m}+\frac {3 b n \left (a+b \log \left (c x^n\right )\right )^2 \text {Li}_3\left (-d f x^m\right )}{m^2}-\frac {6 b^2 n^2 \left (a+b \log \left (c x^n\right )\right ) \text {Li}_4\left (-d f x^m\right )}{m^3}+\frac {6 b^3 n^3 \text {Li}_5\left (-d f x^m\right )}{m^4}\\ \end {align*}

________________________________________________________________________________________

Mathematica [B]  time = 0.41, size = 1035, normalized size = 9.86 \[ -\frac {3}{10} b^3 m n^3 \log ^5(x)+\frac {3}{4} a b^2 m n^2 \log ^4(x)+\frac {3}{4} b^3 m n^2 \log \left (c x^n\right ) \log ^4(x)-\frac {3}{4} b^3 n^3 \log \left (\frac {x^{-m}}{d f}+1\right ) \log ^4(x)+\frac {3}{4} b^3 n^3 \log \left (d f x^m+1\right ) \log ^4(x)-\frac {1}{2} b^3 m n \log ^2\left (c x^n\right ) \log ^3(x)-\frac {1}{2} a^2 b m n \log ^3(x)-a b^2 m n \log \left (c x^n\right ) \log ^3(x)+2 a b^2 n^2 \log \left (\frac {x^{-m}}{d f}+1\right ) \log ^3(x)+2 b^3 n^2 \log \left (c x^n\right ) \log \left (\frac {x^{-m}}{d f}+1\right ) \log ^3(x)-2 a b^2 n^2 \log \left (d f x^m+1\right ) \log ^3(x)-\frac {b^3 n^3 \log \left (-d f x^m\right ) \log \left (d f x^m+1\right ) \log ^3(x)}{m}-2 b^3 n^2 \log \left (c x^n\right ) \log \left (d f x^m+1\right ) \log ^3(x)-\frac {3}{2} b^3 n \log ^2\left (c x^n\right ) \log \left (\frac {x^{-m}}{d f}+1\right ) \log ^2(x)-\frac {3}{2} a^2 b n \log \left (\frac {x^{-m}}{d f}+1\right ) \log ^2(x)-3 a b^2 n \log \left (c x^n\right ) \log \left (\frac {x^{-m}}{d f}+1\right ) \log ^2(x)+\frac {3}{2} b^3 n \log ^2\left (c x^n\right ) \log \left (d f x^m+1\right ) \log ^2(x)+\frac {3}{2} a^2 b n \log \left (d f x^m+1\right ) \log ^2(x)+\frac {3 a b^2 n^2 \log \left (-d f x^m\right ) \log \left (d f x^m+1\right ) \log ^2(x)}{m}+3 a b^2 n \log \left (c x^n\right ) \log \left (d f x^m+1\right ) \log ^2(x)+\frac {3 b^3 n^2 \log \left (-d f x^m\right ) \log \left (c x^n\right ) \log \left (d f x^m+1\right ) \log ^2(x)}{m}-\frac {3 b^3 n \log \left (-d f x^m\right ) \log ^2\left (c x^n\right ) \log \left (d f x^m+1\right ) \log (x)}{m}-\frac {3 a^2 b n \log \left (-d f x^m\right ) \log \left (d f x^m+1\right ) \log (x)}{m}-\frac {6 a b^2 n \log \left (-d f x^m\right ) \log \left (c x^n\right ) \log \left (d f x^m+1\right ) \log (x)}{m}+\frac {b n \left (b^2 n^2 \log ^2(x)-3 b n \left (a+b \log \left (c x^n\right )\right ) \log (x)+3 \left (a+b \log \left (c x^n\right )\right )^2\right ) \text {Li}_2\left (-\frac {x^{-m}}{d f}\right ) \log (x)}{m}+\frac {b^3 \log \left (-d f x^m\right ) \log ^3\left (c x^n\right ) \log \left (d f x^m+1\right )}{m}+\frac {3 a b^2 \log \left (-d f x^m\right ) \log ^2\left (c x^n\right ) \log \left (d f x^m+1\right )}{m}+\frac {a^3 \log \left (-d f x^m\right ) \log \left (d f x^m+1\right )}{m}+\frac {3 a^2 b \log \left (-d f x^m\right ) \log \left (c x^n\right ) \log \left (d f x^m+1\right )}{m}+\frac {\left (a-b n \log (x)+b \log \left (c x^n\right )\right )^3 \text {Li}_2\left (d f x^m+1\right )}{m}+\frac {3 b^3 n \log ^2\left (c x^n\right ) \text {Li}_3\left (-\frac {x^{-m}}{d f}\right )}{m^2}+\frac {3 a^2 b n \text {Li}_3\left (-\frac {x^{-m}}{d f}\right )}{m^2}+\frac {6 a b^2 n \log \left (c x^n\right ) \text {Li}_3\left (-\frac {x^{-m}}{d f}\right )}{m^2}+\frac {6 a b^2 n^2 \text {Li}_4\left (-\frac {x^{-m}}{d f}\right )}{m^3}+\frac {6 b^3 n^2 \log \left (c x^n\right ) \text {Li}_4\left (-\frac {x^{-m}}{d f}\right )}{m^3}+\frac {6 b^3 n^3 \text {Li}_5\left (-\frac {x^{-m}}{d f}\right )}{m^4} \]

Antiderivative was successfully verified.

[In]

Integrate[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^m)])/x,x]

[Out]

-1/2*(a^2*b*m*n*Log[x]^3) + (3*a*b^2*m*n^2*Log[x]^4)/4 - (3*b^3*m*n^3*Log[x]^5)/10 - a*b^2*m*n*Log[x]^3*Log[c*
x^n] + (3*b^3*m*n^2*Log[x]^4*Log[c*x^n])/4 - (b^3*m*n*Log[x]^3*Log[c*x^n]^2)/2 - (3*a^2*b*n*Log[x]^2*Log[1 + 1
/(d*f*x^m)])/2 + 2*a*b^2*n^2*Log[x]^3*Log[1 + 1/(d*f*x^m)] - (3*b^3*n^3*Log[x]^4*Log[1 + 1/(d*f*x^m)])/4 - 3*a
*b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] + 2*b^3*n^2*Log[x]^3*Log[c*x^n]*Log[1 + 1/(d*f*x^m)] - (3*b^3*
n*Log[x]^2*Log[c*x^n]^2*Log[1 + 1/(d*f*x^m)])/2 + (3*a^2*b*n*Log[x]^2*Log[1 + d*f*x^m])/2 - 2*a*b^2*n^2*Log[x]
^3*Log[1 + d*f*x^m] + (3*b^3*n^3*Log[x]^4*Log[1 + d*f*x^m])/4 + (a^3*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m - (3*
a^2*b*n*Log[x]*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + (3*a*b^2*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m
- (b^3*n^3*Log[x]^3*Log[-(d*f*x^m)]*Log[1 + d*f*x^m])/m + 3*a*b^2*n*Log[x]^2*Log[c*x^n]*Log[1 + d*f*x^m] - 2*
b^3*n^2*Log[x]^3*Log[c*x^n]*Log[1 + d*f*x^m] + (3*a^2*b*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m - (6*a*
b^2*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]*Log[1 + d*f*x^m])/m + (3*b^3*n^2*Log[x]^2*Log[-(d*f*x^m)]*Log[c*x^n]*L
og[1 + d*f*x^m])/m + (3*b^3*n*Log[x]^2*Log[c*x^n]^2*Log[1 + d*f*x^m])/2 + (3*a*b^2*Log[-(d*f*x^m)]*Log[c*x^n]^
2*Log[1 + d*f*x^m])/m - (3*b^3*n*Log[x]*Log[-(d*f*x^m)]*Log[c*x^n]^2*Log[1 + d*f*x^m])/m + (b^3*Log[-(d*f*x^m)
]*Log[c*x^n]^3*Log[1 + d*f*x^m])/m + (b*n*Log[x]*(b^2*n^2*Log[x]^2 - 3*b*n*Log[x]*(a + b*Log[c*x^n]) + 3*(a +
b*Log[c*x^n])^2)*PolyLog[2, -(1/(d*f*x^m))])/m + ((a - b*n*Log[x] + b*Log[c*x^n])^3*PolyLog[2, 1 + d*f*x^m])/m
+ (3*a^2*b*n*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (6*a*b^2*n*Log[c*x^n]*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (3*b^3
*n*Log[c*x^n]^2*PolyLog[3, -(1/(d*f*x^m))])/m^2 + (6*a*b^2*n^2*PolyLog[4, -(1/(d*f*x^m))])/m^3 + (6*b^3*n^2*Lo
g[c*x^n]*PolyLog[4, -(1/(d*f*x^m))])/m^3 + (6*b^3*n^3*PolyLog[5, -(1/(d*f*x^m))])/m^4

________________________________________________________________________________________

fricas [C]  time = 0.74, size = 285, normalized size = 2.71 \[ \frac {6 \, b^{3} n^{3} {\rm polylog}\left (5, -d f x^{m}\right ) - {\left (b^{3} m^{3} n^{3} \log \relax (x)^{3} + b^{3} m^{3} \log \relax (c)^{3} + 3 \, a b^{2} m^{3} \log \relax (c)^{2} + 3 \, a^{2} b m^{3} \log \relax (c) + a^{3} m^{3} + 3 \, {\left (b^{3} m^{3} n^{2} \log \relax (c) + a b^{2} m^{3} n^{2}\right )} \log \relax (x)^{2} + 3 \, {\left (b^{3} m^{3} n \log \relax (c)^{2} + 2 \, a b^{2} m^{3} n \log \relax (c) + a^{2} b m^{3} n\right )} \log \relax (x)\right )} {\rm Li}_2\left (-d f x^{m}\right ) - 6 \, {\left (b^{3} m n^{3} \log \relax (x) + b^{3} m n^{2} \log \relax (c) + a b^{2} m n^{2}\right )} {\rm polylog}\left (4, -d f x^{m}\right ) + 3 \, {\left (b^{3} m^{2} n^{3} \log \relax (x)^{2} + b^{3} m^{2} n \log \relax (c)^{2} + 2 \, a b^{2} m^{2} n \log \relax (c) + a^{2} b m^{2} n + 2 \, {\left (b^{3} m^{2} n^{2} \log \relax (c) + a b^{2} m^{2} n^{2}\right )} \log \relax (x)\right )} {\rm polylog}\left (3, -d f x^{m}\right )}{m^{4}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*x^n))^3*log(d*(1/d+f*x^m))/x,x, algorithm="fricas")

[Out]

(6*b^3*n^3*polylog(5, -d*f*x^m) - (b^3*m^3*n^3*log(x)^3 + b^3*m^3*log(c)^3 + 3*a*b^2*m^3*log(c)^2 + 3*a^2*b*m^
3*log(c) + a^3*m^3 + 3*(b^3*m^3*n^2*log(c) + a*b^2*m^3*n^2)*log(x)^2 + 3*(b^3*m^3*n*log(c)^2 + 2*a*b^2*m^3*n*l
og(c) + a^2*b*m^3*n)*log(x))*dilog(-d*f*x^m) - 6*(b^3*m*n^3*log(x) + b^3*m*n^2*log(c) + a*b^2*m*n^2)*polylog(4
, -d*f*x^m) + 3*(b^3*m^2*n^3*log(x)^2 + b^3*m^2*n*log(c)^2 + 2*a*b^2*m^2*n*log(c) + a^2*b*m^2*n + 2*(b^3*m^2*n
^2*log(c) + a*b^2*m^2*n^2)*log(x))*polylog(3, -d*f*x^m))/m^4

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (b \log \left (c x^{n}\right ) + a\right )}^{3} \log \left ({\left (f x^{m} + \frac {1}{d}\right )} d\right )}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*x^n))^3*log(d*(1/d+f*x^m))/x,x, algorithm="giac")

[Out]

integrate((b*log(c*x^n) + a)^3*log((f*x^m + 1/d)*d)/x, x)

________________________________________________________________________________________

maple [C]  time = 1.27, size = 11734, normalized size = 111.75 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*ln(c*x^n)+a)^3*ln(d*(1/d+f*x^m))/x,x)

[Out]

result too large to display

________________________________________________________________________________________

maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {1}{4} \, {\left (b^{3} n^{3} \log \relax (x)^{4} - 4 \, b^{3} \log \relax (x) \log \left (x^{n}\right )^{3} - 4 \, {\left (b^{3} n^{2} \log \relax (c) + a b^{2} n^{2}\right )} \log \relax (x)^{3} + 6 \, {\left (b^{3} n \log \relax (c)^{2} + 2 \, a b^{2} n \log \relax (c) + a^{2} b n\right )} \log \relax (x)^{2} + 6 \, {\left (b^{3} n \log \relax (x)^{2} - 2 \, {\left (b^{3} \log \relax (c) + a b^{2}\right )} \log \relax (x)\right )} \log \left (x^{n}\right )^{2} - 4 \, {\left (b^{3} n^{2} \log \relax (x)^{3} - 3 \, {\left (b^{3} n \log \relax (c) + a b^{2} n\right )} \log \relax (x)^{2} + 3 \, {\left (b^{3} \log \relax (c)^{2} + 2 \, a b^{2} \log \relax (c) + a^{2} b\right )} \log \relax (x)\right )} \log \left (x^{n}\right ) - 4 \, {\left (b^{3} \log \relax (c)^{3} + 3 \, a b^{2} \log \relax (c)^{2} + 3 \, a^{2} b \log \relax (c) + a^{3}\right )} \log \relax (x)\right )} \log \left (d f x^{m} + 1\right ) - \int \frac {4 \, b^{3} d f m x^{m} \log \relax (x) \log \left (x^{n}\right )^{3} - 6 \, {\left (b^{3} d f m n \log \relax (x)^{2} - 2 \, {\left (b^{3} d f m \log \relax (c) + a b^{2} d f m\right )} \log \relax (x)\right )} x^{m} \log \left (x^{n}\right )^{2} + 4 \, {\left (b^{3} d f m n^{2} \log \relax (x)^{3} - 3 \, {\left (b^{3} d f m n \log \relax (c) + a b^{2} d f m n\right )} \log \relax (x)^{2} + 3 \, {\left (b^{3} d f m \log \relax (c)^{2} + 2 \, a b^{2} d f m \log \relax (c) + a^{2} b d f m\right )} \log \relax (x)\right )} x^{m} \log \left (x^{n}\right ) - {\left (b^{3} d f m n^{3} \log \relax (x)^{4} - 4 \, {\left (b^{3} d f m n^{2} \log \relax (c) + a b^{2} d f m n^{2}\right )} \log \relax (x)^{3} + 6 \, {\left (b^{3} d f m n \log \relax (c)^{2} + 2 \, a b^{2} d f m n \log \relax (c) + a^{2} b d f m n\right )} \log \relax (x)^{2} - 4 \, {\left (b^{3} d f m \log \relax (c)^{3} + 3 \, a b^{2} d f m \log \relax (c)^{2} + 3 \, a^{2} b d f m \log \relax (c) + a^{3} d f m\right )} \log \relax (x)\right )} x^{m}}{4 \, {\left (d f x x^{m} + x\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*log(c*x^n))^3*log(d*(1/d+f*x^m))/x,x, algorithm="maxima")

[Out]

-1/4*(b^3*n^3*log(x)^4 - 4*b^3*log(x)*log(x^n)^3 - 4*(b^3*n^2*log(c) + a*b^2*n^2)*log(x)^3 + 6*(b^3*n*log(c)^2
+ 2*a*b^2*n*log(c) + a^2*b*n)*log(x)^2 + 6*(b^3*n*log(x)^2 - 2*(b^3*log(c) + a*b^2)*log(x))*log(x^n)^2 - 4*(b
^3*n^2*log(x)^3 - 3*(b^3*n*log(c) + a*b^2*n)*log(x)^2 + 3*(b^3*log(c)^2 + 2*a*b^2*log(c) + a^2*b)*log(x))*log(
x^n) - 4*(b^3*log(c)^3 + 3*a*b^2*log(c)^2 + 3*a^2*b*log(c) + a^3)*log(x))*log(d*f*x^m + 1) - integrate(1/4*(4*
b^3*d*f*m*x^m*log(x)*log(x^n)^3 - 6*(b^3*d*f*m*n*log(x)^2 - 2*(b^3*d*f*m*log(c) + a*b^2*d*f*m)*log(x))*x^m*log
(x^n)^2 + 4*(b^3*d*f*m*n^2*log(x)^3 - 3*(b^3*d*f*m*n*log(c) + a*b^2*d*f*m*n)*log(x)^2 + 3*(b^3*d*f*m*log(c)^2
+ 2*a*b^2*d*f*m*log(c) + a^2*b*d*f*m)*log(x))*x^m*log(x^n) - (b^3*d*f*m*n^3*log(x)^4 - 4*(b^3*d*f*m*n^2*log(c)
+ a*b^2*d*f*m*n^2)*log(x)^3 + 6*(b^3*d*f*m*n*log(c)^2 + 2*a*b^2*d*f*m*n*log(c) + a^2*b*d*f*m*n)*log(x)^2 - 4*
(b^3*d*f*m*log(c)^3 + 3*a*b^2*d*f*m*log(c)^2 + 3*a^2*b*d*f*m*log(c) + a^3*d*f*m)*log(x))*x^m)/(d*f*x*x^m + x),
x)

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.01 \[ \int \frac {\ln \left (d\,\left (f\,x^m+\frac {1}{d}\right )\right )\,{\left (a+b\,\ln \left (c\,x^n\right )\right )}^3}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(d*(f*x^m + 1/d))*(a + b*log(c*x^n))^3)/x,x)

[Out]

int((log(d*(f*x^m + 1/d))*(a + b*log(c*x^n))^3)/x, x)

________________________________________________________________________________________

sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*ln(c*x**n))**3*ln(d*(1/d+f*x**m))/x,x)

[Out]

Timed out

________________________________________________________________________________________