3.2.7 \(\int \frac {e^6 (-162+198 x-90 x^2-18 x^3-6 x^4-10 x^5-18 x^6-4 x^7)+e^3 (18 x-18 x^2+6 x^4+4 x^5) \log (2)+(e^6 (-36+90 x+72 x^2+18 x^3+30 x^4+54 x^5+12 x^6)+e^3 (-18+18 x-18 x^3-12 x^4) \log (2)) \log (x)+(e^6 (-54 x-30 x^3-54 x^4-12 x^5)+e^3 (18 x^2+12 x^3) \log (2)) \log ^2(x)+(e^6 (-12 x+10 x^2+18 x^3+4 x^4)+e^3 (-6 x-4 x^2) \log (2)) \log ^3(x)}{-x^4+3 x^3 \log (x)-3 x^2 \log ^2(x)+x \log ^3(x)} \, dx\)

Optimal. Leaf size=31 \[ 1+\left (\log (2)+e^3 \left (2-3 x-x^2-\frac {9}{x-\log (x)}\right )\right )^2 \]

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Rubi [F]  time = 1.28, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {e^6 \left (-162+198 x-90 x^2-18 x^3-6 x^4-10 x^5-18 x^6-4 x^7\right )+e^3 \left (18 x-18 x^2+6 x^4+4 x^5\right ) \log (2)+\left (e^6 \left (-36+90 x+72 x^2+18 x^3+30 x^4+54 x^5+12 x^6\right )+e^3 \left (-18+18 x-18 x^3-12 x^4\right ) \log (2)\right ) \log (x)+\left (e^6 \left (-54 x-30 x^3-54 x^4-12 x^5\right )+e^3 \left (18 x^2+12 x^3\right ) \log (2)\right ) \log ^2(x)+\left (e^6 \left (-12 x+10 x^2+18 x^3+4 x^4\right )+e^3 \left (-6 x-4 x^2\right ) \log (2)\right ) \log ^3(x)}{-x^4+3 x^3 \log (x)-3 x^2 \log ^2(x)+x \log ^3(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^6*(-162 + 198*x - 90*x^2 - 18*x^3 - 6*x^4 - 10*x^5 - 18*x^6 - 4*x^7) + E^3*(18*x - 18*x^2 + 6*x^4 + 4*x
^5)*Log[2] + (E^6*(-36 + 90*x + 72*x^2 + 18*x^3 + 30*x^4 + 54*x^5 + 12*x^6) + E^3*(-18 + 18*x - 18*x^3 - 12*x^
4)*Log[2])*Log[x] + (E^6*(-54*x - 30*x^3 - 54*x^4 - 12*x^5) + E^3*(18*x^2 + 12*x^3)*Log[2])*Log[x]^2 + (E^6*(-
12*x + 10*x^2 + 18*x^3 + 4*x^4) + E^3*(-6*x - 4*x^2)*Log[2])*Log[x]^3)/(-x^4 + 3*x^3*Log[x] - 3*x^2*Log[x]^2 +
x*Log[x]^3),x]

[Out]

(2*E^3 - 3*E^3*x - E^3*x^2 + Log[2])^2 + (81*E^6)/(x - Log[x])^2 + 18*E^3*(5*E^3 + Log[2])*Defer[Int][(x - Log
[x])^(-2), x] - 18*E^3*(2*E^3 + Log[2])*Defer[Int][1/(x*(x - Log[x])^2), x] - 36*E^6*Defer[Int][x/(x - Log[x])
^2, x] - 18*E^6*Defer[Int][x^2/(x - Log[x])^2, x] + 54*E^6*Defer[Int][(x - Log[x])^(-1), x] + 36*E^6*Defer[Int
][x/(x - Log[x]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^3 \left (e^3 \left (9-2 x+3 x^2+x^3\right )-x \log (2)+\left (-e^3 \left (-2+3 x+x^2\right )+\log (2)\right ) \log (x)\right ) \left (9-9 x+3 x^3+2 x^4-2 x^2 (3+2 x) \log (x)+x (3+2 x) \log ^2(x)\right )}{x (x-\log (x))^3} \, dx\\ &=\left (2 e^3\right ) \int \frac {\left (e^3 \left (9-2 x+3 x^2+x^3\right )-x \log (2)+\left (-e^3 \left (-2+3 x+x^2\right )+\log (2)\right ) \log (x)\right ) \left (9-9 x+3 x^3+2 x^4-2 x^2 (3+2 x) \log (x)+x (3+2 x) \log ^2(x)\right )}{x (x-\log (x))^3} \, dx\\ &=\left (2 e^3\right ) \int \left ((3+2 x) \left (-2 e^3+3 e^3 x+e^3 x^2-\log (2)\right )-\frac {81 e^3 (-1+x)}{x (x-\log (x))^3}-\frac {9 (-1+x) \left (-2 e^3+3 e^3 x+e^3 x^2-\log (2)\right )}{x (x-\log (x))^2}+\frac {9 e^3 (3+2 x)}{x-\log (x)}\right ) \, dx\\ &=\left (2 e^3\right ) \int (3+2 x) \left (-2 e^3+3 e^3 x+e^3 x^2-\log (2)\right ) \, dx-\left (18 e^3\right ) \int \frac {(-1+x) \left (-2 e^3+3 e^3 x+e^3 x^2-\log (2)\right )}{x (x-\log (x))^2} \, dx+\left (18 e^6\right ) \int \frac {3+2 x}{x-\log (x)} \, dx-\left (162 e^6\right ) \int \frac {-1+x}{x (x-\log (x))^3} \, dx\\ &=\left (2 e^3-3 e^3 x-e^3 x^2+\log (2)\right )^2+\frac {81 e^6}{(x-\log (x))^2}-\left (18 e^3\right ) \int \left (\frac {2 e^3 x}{(x-\log (x))^2}+\frac {e^3 x^2}{(x-\log (x))^2}+\frac {2 e^3+\log (2)}{x (x-\log (x))^2}-\frac {5 e^3 \left (1+\frac {\log (2)}{5 e^3}\right )}{(x-\log (x))^2}\right ) \, dx+\left (18 e^6\right ) \int \left (\frac {3}{x-\log (x)}+\frac {2 x}{x-\log (x)}\right ) \, dx\\ &=\left (2 e^3-3 e^3 x-e^3 x^2+\log (2)\right )^2+\frac {81 e^6}{(x-\log (x))^2}-\left (18 e^6\right ) \int \frac {x^2}{(x-\log (x))^2} \, dx-\left (36 e^6\right ) \int \frac {x}{(x-\log (x))^2} \, dx+\left (36 e^6\right ) \int \frac {x}{x-\log (x)} \, dx+\left (54 e^6\right ) \int \frac {1}{x-\log (x)} \, dx-\left (18 e^3 \left (2 e^3+\log (2)\right )\right ) \int \frac {1}{x (x-\log (x))^2} \, dx+\left (18 e^3 \left (5 e^3+\log (2)\right )\right ) \int \frac {1}{(x-\log (x))^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.11, size = 85, normalized size = 2.74 \begin {gather*} e^3 \left (6 e^3 x^3+e^3 x^4-6 x \left (2 e^3+\log (2)\right )+x^2 \left (5 e^3-\log (4)\right )+\frac {81 e^3}{(x-\log (x))^2}+\frac {18 \left (e^3 \left (-2+3 x+x^2\right )-\log (2)\right )}{x-\log (x)}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^6*(-162 + 198*x - 90*x^2 - 18*x^3 - 6*x^4 - 10*x^5 - 18*x^6 - 4*x^7) + E^3*(18*x - 18*x^2 + 6*x^4
+ 4*x^5)*Log[2] + (E^6*(-36 + 90*x + 72*x^2 + 18*x^3 + 30*x^4 + 54*x^5 + 12*x^6) + E^3*(-18 + 18*x - 18*x^3 -
12*x^4)*Log[2])*Log[x] + (E^6*(-54*x - 30*x^3 - 54*x^4 - 12*x^5) + E^3*(18*x^2 + 12*x^3)*Log[2])*Log[x]^2 + (
E^6*(-12*x + 10*x^2 + 18*x^3 + 4*x^4) + E^3*(-6*x - 4*x^2)*Log[2])*Log[x]^3)/(-x^4 + 3*x^3*Log[x] - 3*x^2*Log[
x]^2 + x*Log[x]^3),x]

[Out]

E^3*(6*E^3*x^3 + E^3*x^4 - 6*x*(2*E^3 + Log[2]) + x^2*(5*E^3 - Log[4]) + (81*E^3)/(x - Log[x])^2 + (18*(E^3*(-
2 + 3*x + x^2) - Log[2]))/(x - Log[x]))

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fricas [B]  time = 0.89, size = 157, normalized size = 5.06 \begin {gather*} -\frac {2 \, {\left (x^{4} + 3 \, x^{3} + 9 \, x\right )} e^{3} \log \relax (2) + {\left (2 \, {\left (x^{2} + 3 \, x\right )} e^{3} \log \relax (2) - {\left (x^{4} + 6 \, x^{3} + 5 \, x^{2} - 12 \, x\right )} e^{6}\right )} \log \relax (x)^{2} - {\left (x^{6} + 6 \, x^{5} + 5 \, x^{4} + 6 \, x^{3} + 54 \, x^{2} - 36 \, x + 81\right )} e^{6} - 2 \, {\left ({\left (2 \, x^{3} + 6 \, x^{2} + 9\right )} e^{3} \log \relax (2) - {\left (x^{5} + 6 \, x^{4} + 5 \, x^{3} - 3 \, x^{2} + 27 \, x - 18\right )} e^{6}\right )} \log \relax (x)}{x^{2} - 2 \, x \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^2-6*x)*exp(3)*log(2)+(4*x^4+18*x^3+10*x^2-12*x)*exp(3)^2)*log(x)^3+((12*x^3+18*x^2)*exp(3)*l
og(2)+(-12*x^5-54*x^4-30*x^3-54*x)*exp(3)^2)*log(x)^2+((-12*x^4-18*x^3+18*x-18)*exp(3)*log(2)+(12*x^6+54*x^5+3
0*x^4+18*x^3+72*x^2+90*x-36)*exp(3)^2)*log(x)+(4*x^5+6*x^4-18*x^2+18*x)*exp(3)*log(2)+(-4*x^7-18*x^6-10*x^5-6*
x^4-18*x^3-90*x^2+198*x-162)*exp(3)^2)/(x*log(x)^3-3*x^2*log(x)^2+3*x^3*log(x)-x^4),x, algorithm="fricas")

[Out]

-(2*(x^4 + 3*x^3 + 9*x)*e^3*log(2) + (2*(x^2 + 3*x)*e^3*log(2) - (x^4 + 6*x^3 + 5*x^2 - 12*x)*e^6)*log(x)^2 -
(x^6 + 6*x^5 + 5*x^4 + 6*x^3 + 54*x^2 - 36*x + 81)*e^6 - 2*((2*x^3 + 6*x^2 + 9)*e^3*log(2) - (x^5 + 6*x^4 + 5*
x^3 - 3*x^2 + 27*x - 18)*e^6)*log(x))/(x^2 - 2*x*log(x) + log(x)^2)

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giac [B]  time = 0.53, size = 229, normalized size = 7.39 \begin {gather*} \frac {x^{6} e^{6} - 2 \, x^{5} e^{6} \log \relax (x) + x^{4} e^{6} \log \relax (x)^{2} + 6 \, x^{5} e^{6} - 2 \, x^{4} e^{3} \log \relax (2) - 12 \, x^{4} e^{6} \log \relax (x) + 4 \, x^{3} e^{3} \log \relax (2) \log \relax (x) + 6 \, x^{3} e^{6} \log \relax (x)^{2} - 2 \, x^{2} e^{3} \log \relax (2) \log \relax (x)^{2} + 5 \, x^{4} e^{6} - 6 \, x^{3} e^{3} \log \relax (2) - 10 \, x^{3} e^{6} \log \relax (x) + 12 \, x^{2} e^{3} \log \relax (2) \log \relax (x) + 5 \, x^{2} e^{6} \log \relax (x)^{2} - 6 \, x e^{3} \log \relax (2) \log \relax (x)^{2} + 6 \, x^{3} e^{6} + 6 \, x^{2} e^{6} \log \relax (x) - 12 \, x e^{6} \log \relax (x)^{2} + 54 \, x^{2} e^{6} - 18 \, x e^{3} \log \relax (2) - 54 \, x e^{6} \log \relax (x) + 18 \, e^{3} \log \relax (2) \log \relax (x) - 36 \, x e^{6} + 36 \, e^{6} \log \relax (x) + 81 \, e^{6}}{x^{2} - 2 \, x \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^2-6*x)*exp(3)*log(2)+(4*x^4+18*x^3+10*x^2-12*x)*exp(3)^2)*log(x)^3+((12*x^3+18*x^2)*exp(3)*l
og(2)+(-12*x^5-54*x^4-30*x^3-54*x)*exp(3)^2)*log(x)^2+((-12*x^4-18*x^3+18*x-18)*exp(3)*log(2)+(12*x^6+54*x^5+3
0*x^4+18*x^3+72*x^2+90*x-36)*exp(3)^2)*log(x)+(4*x^5+6*x^4-18*x^2+18*x)*exp(3)*log(2)+(-4*x^7-18*x^6-10*x^5-6*
x^4-18*x^3-90*x^2+198*x-162)*exp(3)^2)/(x*log(x)^3-3*x^2*log(x)^2+3*x^3*log(x)-x^4),x, algorithm="giac")

[Out]

(x^6*e^6 - 2*x^5*e^6*log(x) + x^4*e^6*log(x)^2 + 6*x^5*e^6 - 2*x^4*e^3*log(2) - 12*x^4*e^6*log(x) + 4*x^3*e^3*
log(2)*log(x) + 6*x^3*e^6*log(x)^2 - 2*x^2*e^3*log(2)*log(x)^2 + 5*x^4*e^6 - 6*x^3*e^3*log(2) - 10*x^3*e^6*log
(x) + 12*x^2*e^3*log(2)*log(x) + 5*x^2*e^6*log(x)^2 - 6*x*e^3*log(2)*log(x)^2 + 6*x^3*e^6 + 6*x^2*e^6*log(x) -
12*x*e^6*log(x)^2 + 54*x^2*e^6 - 18*x*e^3*log(2) - 54*x*e^6*log(x) + 18*e^3*log(2)*log(x) - 36*x*e^6 + 36*e^6
*log(x) + 81*e^6)/(x^2 - 2*x*log(x) + log(x)^2)

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maple [B]  time = 0.06, size = 107, normalized size = 3.45

method	result	size
risch	\({\mathrm e}^{3} x \left (x^{3} {\mathrm e}^{3}+6 x^{2} {\mathrm e}^{3}+5 x \,{\mathrm e}^{3}-2 x \ln \relax (2)-12 \,{\mathrm e}^{3}-6 \ln \relax (2)\right )+\frac {9 \,{\mathrm e}^{3} \left (2 x^{3} {\mathrm e}^{3}-2 \ln \relax (x ) {\mathrm e}^{3} x^{2}+6 x^{2} {\mathrm e}^{3}-6 x \,{\mathrm e}^{3} \ln \relax (x )-4 x \,{\mathrm e}^{3}+4 \ln \relax (x ) {\mathrm e}^{3}-2 x \ln \relax (2)+2 \ln \relax (2) \ln \relax (x )+9 \,{\mathrm e}^{3}\right )}{\left (x -\ln \relax (x )\right )^{2}}\)	\(107\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-4*x^2-6*x)*exp(3)*ln(2)+(4*x^4+18*x^3+10*x^2-12*x)*exp(3)^2)*ln(x)^3+((12*x^3+18*x^2)*exp(3)*ln(2)+(-1
2*x^5-54*x^4-30*x^3-54*x)*exp(3)^2)*ln(x)^2+((-12*x^4-18*x^3+18*x-18)*exp(3)*ln(2)+(12*x^6+54*x^5+30*x^4+18*x^
3+72*x^2+90*x-36)*exp(3)^2)*ln(x)+(4*x^5+6*x^4-18*x^2+18*x)*exp(3)*ln(2)+(-4*x^7-18*x^6-10*x^5-6*x^4-18*x^3-90
*x^2+198*x-162)*exp(3)^2)/(x*ln(x)^3-3*x^2*ln(x)^2+3*x^3*ln(x)-x^4),x,method=_RETURNVERBOSE)

[Out]

exp(3)*x*(x^3*exp(3)+6*x^2*exp(3)+5*x*exp(3)-2*x*ln(2)-12*exp(3)-6*ln(2))+9*exp(3)*(2*x^3*exp(3)-2*ln(x)*exp(3
)*x^2+6*x^2*exp(3)-6*x*exp(3)*ln(x)-4*x*exp(3)+4*ln(x)*exp(3)-2*x*ln(2)+2*ln(2)*ln(x)+9*exp(3))/(x-ln(x))^2

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maxima [B]  time = 0.62, size = 196, normalized size = 6.32 \begin {gather*} \frac {x^{6} e^{6} + 6 \, x^{5} e^{6} - {\left (2 \, e^{3} \log \relax (2) - 5 \, e^{6}\right )} x^{4} - 6 \, {\left (e^{3} \log \relax (2) - e^{6}\right )} x^{3} + 54 \, x^{2} e^{6} + {\left (x^{4} e^{6} + 6 \, x^{3} e^{6} - {\left (2 \, e^{3} \log \relax (2) - 5 \, e^{6}\right )} x^{2} - 6 \, {\left (e^{3} \log \relax (2) + 2 \, e^{6}\right )} x\right )} \log \relax (x)^{2} - 18 \, {\left (e^{3} \log \relax (2) + 2 \, e^{6}\right )} x - 2 \, {\left (x^{5} e^{6} + 6 \, x^{4} e^{6} - {\left (2 \, e^{3} \log \relax (2) - 5 \, e^{6}\right )} x^{3} - 3 \, {\left (2 \, e^{3} \log \relax (2) + e^{6}\right )} x^{2} + 27 \, x e^{6} - 9 \, e^{3} \log \relax (2) - 18 \, e^{6}\right )} \log \relax (x) + 81 \, e^{6}}{x^{2} - 2 \, x \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x^2-6*x)*exp(3)*log(2)+(4*x^4+18*x^3+10*x^2-12*x)*exp(3)^2)*log(x)^3+((12*x^3+18*x^2)*exp(3)*l
og(2)+(-12*x^5-54*x^4-30*x^3-54*x)*exp(3)^2)*log(x)^2+((-12*x^4-18*x^3+18*x-18)*exp(3)*log(2)+(12*x^6+54*x^5+3
0*x^4+18*x^3+72*x^2+90*x-36)*exp(3)^2)*log(x)+(4*x^5+6*x^4-18*x^2+18*x)*exp(3)*log(2)+(-4*x^7-18*x^6-10*x^5-6*
x^4-18*x^3-90*x^2+198*x-162)*exp(3)^2)/(x*log(x)^3-3*x^2*log(x)^2+3*x^3*log(x)-x^4),x, algorithm="maxima")

[Out]

(x^6*e^6 + 6*x^5*e^6 - (2*e^3*log(2) - 5*e^6)*x^4 - 6*(e^3*log(2) - e^6)*x^3 + 54*x^2*e^6 + (x^4*e^6 + 6*x^3*e
^6 - (2*e^3*log(2) - 5*e^6)*x^2 - 6*(e^3*log(2) + 2*e^6)*x)*log(x)^2 - 18*(e^3*log(2) + 2*e^6)*x - 2*(x^5*e^6
+ 6*x^4*e^6 - (2*e^3*log(2) - 5*e^6)*x^3 - 3*(2*e^3*log(2) + e^6)*x^2 + 27*x*e^6 - 9*e^3*log(2) - 18*e^6)*log(
x) + 81*e^6)/(x^2 - 2*x*log(x) + log(x)^2)

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mupad [B]  time = 0.94, size = 231, normalized size = 7.45 \begin {gather*} \frac {{\mathrm {e}}^6\,x^8-2\,{\mathrm {e}}^6\,x^7\,\ln \relax (x)+6\,{\mathrm {e}}^6\,x^7+{\mathrm {e}}^6\,x^6\,{\ln \relax (x)}^2-12\,{\mathrm {e}}^6\,x^6\,\ln \relax (x)+\left (5\,{\mathrm {e}}^6-2\,{\mathrm {e}}^3\,\ln \relax (2)\right )\,x^6+6\,{\mathrm {e}}^6\,x^5\,{\ln \relax (x)}^2+\left (4\,{\mathrm {e}}^3\,\ln \relax (2)-10\,{\mathrm {e}}^6\right )\,x^5\,\ln \relax (x)+6\,{\mathrm {e}}^3\,\left ({\mathrm {e}}^3-\ln \relax (2)\right )\,x^5+\left (5\,{\mathrm {e}}^6-2\,{\mathrm {e}}^3\,\ln \relax (2)\right )\,x^4\,{\ln \relax (x)}^2+\left (6\,{\mathrm {e}}^6+12\,{\mathrm {e}}^3\,\ln \relax (2)\right )\,x^4\,\ln \relax (x)+54\,{\mathrm {e}}^6\,x^4+\left (-12\,{\mathrm {e}}^6-6\,{\mathrm {e}}^3\,\ln \relax (2)\right )\,x^3\,{\ln \relax (x)}^2-54\,{\mathrm {e}}^6\,x^3\,\ln \relax (x)-18\,{\mathrm {e}}^3\,\left (2\,{\mathrm {e}}^3+\ln \relax (2)\right )\,x^3+18\,{\mathrm {e}}^3\,\left (2\,{\mathrm {e}}^3+\ln \relax (2)\right )\,x^2\,\ln \relax (x)+81\,{\mathrm {e}}^6\,x^2}{x^4-2\,x^3\,\ln \relax (x)+x^2\,{\ln \relax (x)}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)^3*(exp(6)*(10*x^2 - 12*x + 18*x^3 + 4*x^4) - exp(3)*log(2)*(6*x + 4*x^2)) - exp(6)*(90*x^2 - 198*x
+ 18*x^3 + 6*x^4 + 10*x^5 + 18*x^6 + 4*x^7 + 162) + log(x)*(exp(6)*(90*x + 72*x^2 + 18*x^3 + 30*x^4 + 54*x^5
+ 12*x^6 - 36) - exp(3)*log(2)*(18*x^3 - 18*x + 12*x^4 + 18)) - log(x)^2*(exp(6)*(54*x + 30*x^3 + 54*x^4 + 12*
x^5) - exp(3)*log(2)*(18*x^2 + 12*x^3)) + exp(3)*log(2)*(18*x - 18*x^2 + 6*x^4 + 4*x^5))/(x*log(x)^3 + 3*x^3*l
og(x) - 3*x^2*log(x)^2 - x^4),x)

[Out]

(x^6*(5*exp(6) - 2*exp(3)*log(2)) + 81*x^2*exp(6) + 54*x^4*exp(6) + 6*x^7*exp(6) + x^8*exp(6) - 18*x^3*exp(3)*
(2*exp(3) + log(2)) + 6*x^5*exp(3)*(exp(3) - log(2)) - x^5*log(x)*(10*exp(6) - 4*exp(3)*log(2)) + x^4*log(x)*(
6*exp(6) + 12*exp(3)*log(2)) - 54*x^3*exp(6)*log(x) - 12*x^6*exp(6)*log(x) - 2*x^7*exp(6)*log(x) + x^4*log(x)^
2*(5*exp(6) - 2*exp(3)*log(2)) - x^3*log(x)^2*(12*exp(6) + 6*exp(3)*log(2)) + 6*x^5*exp(6)*log(x)^2 + x^6*exp(
6)*log(x)^2 + 18*x^2*exp(3)*log(x)*(2*exp(3) + log(2)))/(x^2*log(x)^2 - 2*x^3*log(x) + x^4)

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sympy [B]  time = 0.26, size = 134, normalized size = 4.32 \begin {gather*} x^{4} e^{6} + 6 x^{3} e^{6} + x^{2} \left (- 2 e^{3} \log {\relax (2 )} + 5 e^{6}\right ) + x \left (- 12 e^{6} - 6 e^{3} \log {\relax (2 )}\right ) + \frac {18 x^{3} e^{6} + 54 x^{2} e^{6} - 36 x e^{6} - 18 x e^{3} \log {\relax (2 )} + \left (- 18 x^{2} e^{6} - 54 x e^{6} + 18 e^{3} \log {\relax (2 )} + 36 e^{6}\right ) \log {\relax (x )} + 81 e^{6}}{x^{2} - 2 x \log {\relax (x )} + \log {\relax (x )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-4*x**2-6*x)*exp(3)*ln(2)+(4*x**4+18*x**3+10*x**2-12*x)*exp(3)**2)*ln(x)**3+((12*x**3+18*x**2)*ex
p(3)*ln(2)+(-12*x**5-54*x**4-30*x**3-54*x)*exp(3)**2)*ln(x)**2+((-12*x**4-18*x**3+18*x-18)*exp(3)*ln(2)+(12*x*
*6+54*x**5+30*x**4+18*x**3+72*x**2+90*x-36)*exp(3)**2)*ln(x)+(4*x**5+6*x**4-18*x**2+18*x)*exp(3)*ln(2)+(-4*x**
7-18*x**6-10*x**5-6*x**4-18*x**3-90*x**2+198*x-162)*exp(3)**2)/(x*ln(x)**3-3*x**2*ln(x)**2+3*x**3*ln(x)-x**4),
x)

[Out]

x**4*exp(6) + 6*x**3*exp(6) + x**2*(-2*exp(3)*log(2) + 5*exp(6)) + x*(-12*exp(6) - 6*exp(3)*log(2)) + (18*x**3
*exp(6) + 54*x**2*exp(6) - 36*x*exp(6) - 18*x*exp(3)*log(2) + (-18*x**2*exp(6) - 54*x*exp(6) + 18*exp(3)*log(2
) + 36*exp(6))*log(x) + 81*exp(6))/(x**2 - 2*x*log(x) + log(x)**2)

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