3.14.11 \(\int \frac {e^{-1-3 x} \log ^2(-x+x^2) ((-9+18 x) \log (x)+(-3+3 x+(9-9 x^2) \log (x)) \log (-x+x^2))}{-x^4+x^5} \, dx\)

Optimal. Leaf size=26 \[ \frac {3 e^{-1+3 \left (-x+\log \left (\log \left (-x+x^2\right )\right )\right )} \log (x)}{x^3} \]

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Rubi [F]  time = 5.70, 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^{-1-3 x} \log ^2\left (-x+x^2\right ) \left ((-9+18 x) \log (x)+\left (-3+3 x+\left (9-9 x^2\right ) \log (x)\right ) \log \left (-x+x^2\right )\right )}{-x^4+x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-1 - 3*x)*Log[-x + x^2]^2*((-9 + 18*x)*Log[x] + (-3 + 3*x + (9 - 9*x^2)*Log[x])*Log[-x + x^2]))/(-x^4
+ x^5),x]

[Out]

9*Defer[Int][(E^(-1 - 3*x)*Log[x]*Log[(-1 + x)*x]^2)/(-1 + x), x] + 9*Defer[Int][(E^(-1 - 3*x)*Log[x]*Log[(-1
+ x)*x]^2)/x^4, x] - 9*Defer[Int][(E^(-1 - 3*x)*Log[x]*Log[(-1 + x)*x]^2)/x^3, x] - 9*Defer[Int][(E^(-1 - 3*x)
*Log[x]*Log[(-1 + x)*x]^2)/x^2, x] - 9*Defer[Int][(E^(-1 - 3*x)*Log[x]*Log[(-1 + x)*x]^2)/x, x] + 3*Defer[Int]
[(E^(-1 - 3*x)*Log[(-1 + x)*x]^3)/x^4, x] - 9*Defer[Int][(E^(-1 - 3*x)*Log[x]*Log[(-1 + x)*x]^3)/x^4, x] - 9*D
efer[Int][(E^(-1 - 3*x)*Log[x]*Log[(-1 + x)*x]^3)/x^3, x]

Rubi steps

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

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Mathematica [A]  time = 0.40, size = 22, normalized size = 0.85 \begin {gather*} \frac {3 e^{-1-3 x} \log (x) \log ^3((-1+x) x)}{x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-1 - 3*x)*Log[-x + x^2]^2*((-9 + 18*x)*Log[x] + (-3 + 3*x + (9 - 9*x^2)*Log[x])*Log[-x + x^2]))/
(-x^4 + x^5),x]

[Out]

(3*E^(-1 - 3*x)*Log[x]*Log[(-1 + x)*x]^3)/x^3

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fricas [A]  time = 1.14, size = 24, normalized size = 0.92 \begin {gather*} \frac {3 \, e^{\left (-3 \, x + 3 \, \log \left (\log \left (x^{2} - x\right )\right ) - 1\right )} \log \relax (x)}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x^2+9)*log(x)+3*x-3)*log(x^2-x)+(18*x-9)*log(x))*exp(3*log(log(x^2-x))-3*x)/(x^5-x^4)/exp(1)/l
og(x^2-x),x, algorithm="fricas")

[Out]

3*e^(-3*x + 3*log(log(x^2 - x)) - 1)*log(x)/x^3

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {3 \, {\left ({\left (3 \, {\left (x^{2} - 1\right )} \log \relax (x) - x + 1\right )} \log \left (x^{2} - x\right ) - 3 \, {\left (2 \, x - 1\right )} \log \relax (x)\right )} e^{\left (-3 \, x + 3 \, \log \left (\log \left (x^{2} - x\right )\right ) - 1\right )}}{{\left (x^{5} - x^{4}\right )} \log \left (x^{2} - x\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x^2+9)*log(x)+3*x-3)*log(x^2-x)+(18*x-9)*log(x))*exp(3*log(log(x^2-x))-3*x)/(x^5-x^4)/exp(1)/l
og(x^2-x),x, algorithm="giac")

[Out]

integrate(-3*((3*(x^2 - 1)*log(x) - x + 1)*log(x^2 - x) - 3*(2*x - 1)*log(x))*e^(-3*x + 3*log(log(x^2 - x)) -
1)/((x^5 - x^4)*log(x^2 - x)), x)

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maple [C]  time = 0.59, size = 1414, normalized size = 54.38

method	result	size
risch	\(-\frac {3 i \left (\ln \left (x -1\right )+\ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x \left (x -1\right )\right ) \left (-\mathrm {csgn}\left (i x \left (x -1\right )\right )+\mathrm {csgn}\left (i x \right )\right ) \left (-\mathrm {csgn}\left (i x \left (x -1\right )\right )+\mathrm {csgn}\left (i \left (x -1\right )\right )\right )}{2}\right )^{3} \left (8 \ln \relax (x )^{3}+24 \ln \relax (x )^{2} \ln \left (x -1\right )+24 \ln \relax (x ) \ln \left (x -1\right )^{2}+3 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{7}-3 i \pi ^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{8}-i \pi ^{3} \mathrm {csgn}\left (i \left (x -1\right )\right )^{3} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{6}-6 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \ln \relax (x )-6 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \ln \left (x -1\right )+12 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5} \ln \relax (x )+12 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5} \ln \left (x -1\right )-6 \pi ^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \ln \relax (x )-6 \pi ^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \ln \left (x -1\right )+12 \pi ^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5} \ln \relax (x )+12 \pi ^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5} \ln \left (x -1\right )+3 i \pi ^{3} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{7}-3 i \pi ^{3} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{8}-12 i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \relax (x )^{2}-12 i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \left (x -1\right )^{2}-i \pi ^{3} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{6}-3 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{3} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4}+9 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5}-9 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{6}+3 i \pi ^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right )^{3} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5}-9 i \pi ^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{6}+9 i \pi ^{3} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{7}+12 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \relax (x )^{2}+12 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \left (x -1\right )^{2}+12 i \pi \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \relax (x )^{2}+12 i \pi \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \left (x -1\right )^{2}-24 i \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \relax (x ) \ln \left (x -1\right )-6 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \relax (x )-6 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \left (x -1\right )+12 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \relax (x )+12 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \left (x -1\right )+12 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \relax (x )+12 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3} \ln \left (x -1\right )-24 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \ln \relax (x )-24 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4} \ln \left (x -1\right )-24 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right ) \ln \relax (x ) \ln \left (x -1\right )-6 \pi ^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{6} \ln \relax (x )-6 \pi ^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{6} \ln \left (x -1\right )+i \pi ^{3} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{9}-12 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right ) \ln \relax (x )^{2}-12 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right ) \ln \left (x -1\right )^{2}+24 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \relax (x ) \ln \left (x -1\right )+24 i \pi \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2} \ln \relax (x ) \ln \left (x -1\right )+i \pi ^{3} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i \left (x -1\right )\right )^{3} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}-3 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{4}+3 i \pi ^{3} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{5}+8 \ln \left (x -1\right )^{3}\right ) \ln \relax (x ) {\mathrm e}^{-3 x -1}}{\left (2 i \ln \relax (x )+2 i \ln \left (x -1\right )+\pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}+\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}\right )^{3} x^{3}}\)	\(1414\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-9*x^2+9)*ln(x)+3*x-3)*ln(x^2-x)+(18*x-9)*ln(x))*exp(3*ln(ln(x^2-x))-3*x)/(x^5-x^4)/exp(1)/ln(x^2-x),x,
method=_RETURNVERBOSE)

[Out]

-3*I*(ln(x-1)+ln(x)-1/2*I*Pi*csgn(I*x*(x-1))*(-csgn(I*x*(x-1))+csgn(I*x))*(-csgn(I*x*(x-1))+csgn(I*(x-1))))^3/
(2*I*ln(x)+2*I*ln(x-1)+Pi*csgn(I*x*(x-1))^3+Pi*csgn(I*x)*csgn(I*(x-1))*csgn(I*x*(x-1))-Pi*csgn(I*x)*csgn(I*x*(
x-1))^2-Pi*csgn(I*(x-1))*csgn(I*x*(x-1))^2)^3/x^3*(8*ln(x)^3+24*ln(x)^2*ln(x-1)+24*ln(x)*ln(x-1)^2-6*Pi^2*csgn
(I*x)^2*csgn(I*x*(x-1))^4*ln(x)-6*Pi^2*csgn(I*x)^2*csgn(I*x*(x-1))^4*ln(x-1)+12*Pi^2*csgn(I*x)*csgn(I*x*(x-1))
^5*ln(x)+12*Pi^2*csgn(I*x)*csgn(I*x*(x-1))^5*ln(x-1)-6*Pi^2*csgn(I*(x-1))^2*csgn(I*x*(x-1))^4*ln(x)-6*Pi^2*csg
n(I*(x-1))^2*csgn(I*x*(x-1))^4*ln(x-1)+12*Pi^2*csgn(I*(x-1))*csgn(I*x*(x-1))^5*ln(x)+12*Pi^2*csgn(I*(x-1))*csg
n(I*x*(x-1))^5*ln(x-1)+3*I*Pi^3*csgn(I*(x-1))^2*csgn(I*x*(x-1))^7-3*I*Pi^3*csgn(I*(x-1))*csgn(I*x*(x-1))^8-12*
I*Pi*csgn(I*x*(x-1))^3*ln(x)^2-12*I*Pi*csgn(I*x*(x-1))^3*ln(x-1)^2-I*Pi^3*csgn(I*x)^3*csgn(I*x*(x-1))^6+3*I*Pi
^3*csgn(I*x)^2*csgn(I*x*(x-1))^7-3*I*Pi^3*csgn(I*x)*csgn(I*x*(x-1))^8-I*Pi^3*csgn(I*(x-1))^3*csgn(I*x*(x-1))^6
+I*Pi^3*csgn(I*x)^3*csgn(I*(x-1))^3*csgn(I*x*(x-1))^3-3*I*Pi^3*csgn(I*x)^3*csgn(I*(x-1))^2*csgn(I*x*(x-1))^4+3
*I*Pi^3*csgn(I*x)^3*csgn(I*(x-1))*csgn(I*x*(x-1))^5-3*I*Pi^3*csgn(I*x)^2*csgn(I*(x-1))^3*csgn(I*x*(x-1))^4+9*I
*Pi^3*csgn(I*x)^2*csgn(I*(x-1))^2*csgn(I*x*(x-1))^5-9*I*Pi^3*csgn(I*x)^2*csgn(I*(x-1))*csgn(I*x*(x-1))^6+3*I*P
i^3*csgn(I*x)*csgn(I*(x-1))^3*csgn(I*x*(x-1))^5-9*I*Pi^3*csgn(I*x)*csgn(I*(x-1))^2*csgn(I*x*(x-1))^6+9*I*Pi^3*
csgn(I*x)*csgn(I*(x-1))*csgn(I*x*(x-1))^7+12*I*Pi*csgn(I*x)*csgn(I*x*(x-1))^2*ln(x)^2+12*I*Pi*csgn(I*x)*csgn(I
*x*(x-1))^2*ln(x-1)^2+12*I*Pi*csgn(I*(x-1))*csgn(I*x*(x-1))^2*ln(x)^2+12*I*Pi*csgn(I*(x-1))*csgn(I*x*(x-1))^2*
ln(x-1)^2-24*I*Pi*csgn(I*x*(x-1))^3*ln(x)*ln(x-1)-6*Pi^2*csgn(I*x)^2*csgn(I*(x-1))^2*csgn(I*x*(x-1))^2*ln(x)-6
*Pi^2*csgn(I*x)^2*csgn(I*(x-1))^2*csgn(I*x*(x-1))^2*ln(x-1)+12*Pi^2*csgn(I*x)^2*csgn(I*(x-1))*csgn(I*x*(x-1))^
3*ln(x)+12*Pi^2*csgn(I*x)^2*csgn(I*(x-1))*csgn(I*x*(x-1))^3*ln(x-1)+12*Pi^2*csgn(I*x)*csgn(I*(x-1))^2*csgn(I*x
*(x-1))^3*ln(x)+12*Pi^2*csgn(I*x)*csgn(I*(x-1))^2*csgn(I*x*(x-1))^3*ln(x-1)-24*Pi^2*csgn(I*x)*csgn(I*(x-1))*cs
gn(I*x*(x-1))^4*ln(x)-24*Pi^2*csgn(I*x)*csgn(I*(x-1))*csgn(I*x*(x-1))^4*ln(x-1)-24*I*Pi*csgn(I*x)*csgn(I*(x-1)
)*csgn(I*x*(x-1))*ln(x)*ln(x-1)+8*ln(x-1)^3-12*I*Pi*csgn(I*x)*csgn(I*(x-1))*csgn(I*x*(x-1))*ln(x)^2-6*Pi^2*csg
n(I*x*(x-1))^6*ln(x)-6*Pi^2*csgn(I*x*(x-1))^6*ln(x-1)+I*Pi^3*csgn(I*x*(x-1))^9-12*I*Pi*csgn(I*x)*csgn(I*(x-1))
*csgn(I*x*(x-1))*ln(x-1)^2+24*I*Pi*csgn(I*x)*csgn(I*x*(x-1))^2*ln(x)*ln(x-1)+24*I*Pi*csgn(I*(x-1))*csgn(I*x*(x
-1))^2*ln(x)*ln(x-1))*ln(x)*exp(-3*x-1)

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maxima [B]  time = 0.53, size = 60, normalized size = 2.31 \begin {gather*} \frac {3 \, {\left (e^{\left (-3 \, x\right )} \log \left (x - 1\right )^{3} \log \relax (x) + 3 \, e^{\left (-3 \, x\right )} \log \left (x - 1\right )^{2} \log \relax (x)^{2} + 3 \, e^{\left (-3 \, x\right )} \log \left (x - 1\right ) \log \relax (x)^{3} + e^{\left (-3 \, x\right )} \log \relax (x)^{4}\right )} e^{\left (-1\right )}}{x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x^2+9)*log(x)+3*x-3)*log(x^2-x)+(18*x-9)*log(x))*exp(3*log(log(x^2-x))-3*x)/(x^5-x^4)/exp(1)/l
og(x^2-x),x, algorithm="maxima")

[Out]

3*(e^(-3*x)*log(x - 1)^3*log(x) + 3*e^(-3*x)*log(x - 1)^2*log(x)^2 + 3*e^(-3*x)*log(x - 1)*log(x)^3 + e^(-3*x)
*log(x)^4)*e^(-1)/x^3

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {{\mathrm {e}}^{-1}\,{\mathrm {e}}^{3\,\ln \left (\ln \left (x^2-x\right )\right )-3\,x}\,\left (\ln \relax (x)\,\left (18\,x-9\right )-\ln \left (x^2-x\right )\,\left (\ln \relax (x)\,\left (9\,x^2-9\right )-3\,x+3\right )\right )}{\ln \left (x^2-x\right )\,\left (x^4-x^5\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-1)*exp(3*log(log(x^2 - x)) - 3*x)*(log(x)*(18*x - 9) - log(x^2 - x)*(log(x)*(9*x^2 - 9) - 3*x + 3))
)/(log(x^2 - x)*(x^4 - x^5)),x)

[Out]

int(-(exp(-1)*exp(3*log(log(x^2 - x)) - 3*x)*(log(x)*(18*x - 9) - log(x^2 - x)*(log(x)*(9*x^2 - 9) - 3*x + 3))
)/(log(x^2 - x)*(x^4 - x^5)), x)

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sympy [A]  time = 0.44, size = 24, normalized size = 0.92 \begin {gather*} \frac {3 e^{- 3 x} \log {\relax (x )} \log {\left (x^{2} - x \right )}^{3}}{e x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-9*x**2+9)*ln(x)+3*x-3)*ln(x**2-x)+(18*x-9)*ln(x))*exp(3*ln(ln(x**2-x))-3*x)/(x**5-x**4)/exp(1)/l
n(x**2-x),x)

[Out]

3*exp(-1)*exp(-3*x)*log(x)*log(x**2 - x)**3/x**3

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