3.5.11 \(\int \frac {-x-x^2+4 x^3+e^4 (-2+2 x)+(2-4 x+e^4 (-2 x+2 x^2)) \log (x)+e^8 (-x+x^2) \log ^2(x)+(2-2 x-4 x^2+2 x^3+2 x^4+(2 x-2 x^2+e^4 (-2 x^3+2 x^4)) \log (x)+e^4 (2 x-2 x^2) \log ^2(x)) \log (-x+x^2)+(-x^5+x^6+(2 x^3-2 x^4) \log (x)+(-x+x^2) \log ^2(x)) \log ^2(-x+x^2)}{-x+x^2+e^4 (-2 x+2 x^2) \log (x)+e^8 (-x+x^2) \log ^2(x)+(-2 x^3+2 x^4+(2 x-2 x^2+e^4 (-2 x^3+2 x^4)) \log (x)+e^4 (2 x-2 x^2) \log ^2(x)) \log (-x+x^2)+(-x^5+x^6+(2 x^3-2 x^4) \log (x)+(-x+x^2) \log ^2(x)) \log ^2(-x+x^2)} \, dx\)

Optimal. Leaf size=32 \[ -3+x-\frac {2}{1+e^4 \log (x)+\left (x^2-\log (x)\right ) \log \left (-x+x^2\right )} \]

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Rubi [F]  time = 36.63, 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 {-x-x^2+4 x^3+e^4 (-2+2 x)+\left (2-4 x+e^4 \left (-2 x+2 x^2\right )\right ) \log (x)+e^8 \left (-x+x^2\right ) \log ^2(x)+\left (2-2 x-4 x^2+2 x^3+2 x^4+\left (2 x-2 x^2+e^4 \left (-2 x^3+2 x^4\right )\right ) \log (x)+e^4 \left (2 x-2 x^2\right ) \log ^2(x)\right ) \log \left (-x+x^2\right )+\left (-x^5+x^6+\left (2 x^3-2 x^4\right ) \log (x)+\left (-x+x^2\right ) \log ^2(x)\right ) \log ^2\left (-x+x^2\right )}{-x+x^2+e^4 \left (-2 x+2 x^2\right ) \log (x)+e^8 \left (-x+x^2\right ) \log ^2(x)+\left (-2 x^3+2 x^4+\left (2 x-2 x^2+e^4 \left (-2 x^3+2 x^4\right )\right ) \log (x)+e^4 \left (2 x-2 x^2\right ) \log ^2(x)\right ) \log \left (-x+x^2\right )+\left (-x^5+x^6+\left (2 x^3-2 x^4\right ) \log (x)+\left (-x+x^2\right ) \log ^2(x)\right ) \log ^2\left (-x+x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-x - x^2 + 4*x^3 + E^4*(-2 + 2*x) + (2 - 4*x + E^4*(-2*x + 2*x^2))*Log[x] + E^8*(-x + x^2)*Log[x]^2 + (2
- 2*x - 4*x^2 + 2*x^3 + 2*x^4 + (2*x - 2*x^2 + E^4*(-2*x^3 + 2*x^4))*Log[x] + E^4*(2*x - 2*x^2)*Log[x]^2)*Log[
-x + x^2] + (-x^5 + x^6 + (2*x^3 - 2*x^4)*Log[x] + (-x + x^2)*Log[x]^2)*Log[-x + x^2]^2)/(-x + x^2 + E^4*(-2*x
+ 2*x^2)*Log[x] + E^8*(-x + x^2)*Log[x]^2 + (-2*x^3 + 2*x^4 + (2*x - 2*x^2 + E^4*(-2*x^3 + 2*x^4))*Log[x] + E
^4*(2*x - 2*x^2)*Log[x]^2)*Log[-x + x^2] + (-x^5 + x^6 + (2*x^3 - 2*x^4)*Log[x] + (-x + x^2)*Log[x]^2)*Log[-x
+ x^2]^2),x]

[Out]

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^4+\left (1-2 e^4\right ) x+x^2-4 x^3-(-1+x) x \log ^2(x) \left (e^4-\log ((-1+x) x)\right )^2-2 \left (1-x-2 x^2+x^3+x^4\right ) \log ((-1+x) x)-(-1+x) x^5 \log ^2((-1+x) x)-2 \log (x) \left (1-\left (2+e^4\right ) x+e^4 x^2+x \left (1-x-e^4 x^2+e^4 x^3\right ) \log ((-1+x) x)-(-1+x) x^3 \log ^2((-1+x) x)\right )}{(1-x) x \left (1+\log (x) \left (e^4-\log ((-1+x) x)\right )+x^2 \log ((-1+x) x)\right )^2} \, dx\\ &=\int \left (1+\frac {2 \left (1-x-2 \left (1-\frac {e^4}{2}\right ) x^2+2 \left (1-\frac {e^4}{2}\right ) x^3+x^4-2 x^5-2 \left (1+e^4\right ) x^2 \log (x)+4 \left (1+\frac {e^4}{2}\right ) x^3 \log (x)+\log ^2(x)-2 x \log ^2(x)\right )}{(1-x) x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )^2}+\frac {2 \left (-1+2 x^2\right )}{x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )}\right ) \, dx\\ &=x+2 \int \frac {1-x-2 \left (1-\frac {e^4}{2}\right ) x^2+2 \left (1-\frac {e^4}{2}\right ) x^3+x^4-2 x^5-2 \left (1+e^4\right ) x^2 \log (x)+4 \left (1+\frac {e^4}{2}\right ) x^3 \log (x)+\log ^2(x)-2 x \log ^2(x)}{(1-x) x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )^2} \, dx+2 \int \frac {-1+2 x^2}{x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )} \, dx\\ &=x+2 \int \left (\frac {1-x-2 \left (1-\frac {e^4}{2}\right ) x^2+2 \left (1-\frac {e^4}{2}\right ) x^3+x^4-2 x^5-2 \left (1+e^4\right ) x^2 \log (x)+4 \left (1+\frac {e^4}{2}\right ) x^3 \log (x)+\log ^2(x)-2 x \log ^2(x)}{(1-x) \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )^2}+\frac {1-x-2 \left (1-\frac {e^4}{2}\right ) x^2+2 \left (1-\frac {e^4}{2}\right ) x^3+x^4-2 x^5-2 \left (1+e^4\right ) x^2 \log (x)+4 \left (1+\frac {e^4}{2}\right ) x^3 \log (x)+\log ^2(x)-2 x \log ^2(x)}{x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )^2}\right ) \, dx+2 \int \left (-\frac {1}{x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )}+\frac {2 x}{\left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )}\right ) \, dx\\ &=x+2 \int \frac {1-x-2 \left (1-\frac {e^4}{2}\right ) x^2+2 \left (1-\frac {e^4}{2}\right ) x^3+x^4-2 x^5-2 \left (1+e^4\right ) x^2 \log (x)+4 \left (1+\frac {e^4}{2}\right ) x^3 \log (x)+\log ^2(x)-2 x \log ^2(x)}{(1-x) \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )^2} \, dx+2 \int \frac {1-x-2 \left (1-\frac {e^4}{2}\right ) x^2+2 \left (1-\frac {e^4}{2}\right ) x^3+x^4-2 x^5-2 \left (1+e^4\right ) x^2 \log (x)+4 \left (1+\frac {e^4}{2}\right ) x^3 \log (x)+\log ^2(x)-2 x \log ^2(x)}{x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )^2} \, dx-2 \int \frac {1}{x \left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )} \, dx+4 \int \frac {x}{\left (x^2-\log (x)\right ) \left (1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 34, normalized size = 1.06 \begin {gather*} x-\frac {2}{1+e^4 \log (x)+x^2 \log ((-1+x) x)-\log (x) \log ((-1+x) x)} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-x - x^2 + 4*x^3 + E^4*(-2 + 2*x) + (2 - 4*x + E^4*(-2*x + 2*x^2))*Log[x] + E^8*(-x + x^2)*Log[x]^2
+ (2 - 2*x - 4*x^2 + 2*x^3 + 2*x^4 + (2*x - 2*x^2 + E^4*(-2*x^3 + 2*x^4))*Log[x] + E^4*(2*x - 2*x^2)*Log[x]^2
)*Log[-x + x^2] + (-x^5 + x^6 + (2*x^3 - 2*x^4)*Log[x] + (-x + x^2)*Log[x]^2)*Log[-x + x^2]^2)/(-x + x^2 + E^4
*(-2*x + 2*x^2)*Log[x] + E^8*(-x + x^2)*Log[x]^2 + (-2*x^3 + 2*x^4 + (2*x - 2*x^2 + E^4*(-2*x^3 + 2*x^4))*Log[
x] + E^4*(2*x - 2*x^2)*Log[x]^2)*Log[-x + x^2] + (-x^5 + x^6 + (2*x^3 - 2*x^4)*Log[x] + (-x + x^2)*Log[x]^2)*L
og[-x + x^2]^2),x]

[Out]

x - 2/(1 + E^4*Log[x] + x^2*Log[(-1 + x)*x] - Log[x]*Log[(-1 + x)*x])

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fricas [A]  time = 1.30, size = 54, normalized size = 1.69 \begin {gather*} \frac {x e^{4} \log \relax (x) + {\left (x^{3} - x \log \relax (x)\right )} \log \left (x^{2} - x\right ) + x - 2}{{\left (x^{2} - \log \relax (x)\right )} \log \left (x^{2} - x\right ) + e^{4} \log \relax (x) + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-x)*log(x)^2+(-2*x^4+2*x^3)*log(x)+x^6-x^5)*log(x^2-x)^2+((-2*x^2+2*x)*exp(4)*log(x)^2+((2*x^4
-2*x^3)*exp(4)-2*x^2+2*x)*log(x)+2*x^4+2*x^3-4*x^2-2*x+2)*log(x^2-x)+(x^2-x)*exp(4)^2*log(x)^2+((2*x^2-2*x)*ex
p(4)-4*x+2)*log(x)+(2*x-2)*exp(4)+4*x^3-x^2-x)/(((x^2-x)*log(x)^2+(-2*x^4+2*x^3)*log(x)+x^6-x^5)*log(x^2-x)^2+
((-2*x^2+2*x)*exp(4)*log(x)^2+((2*x^4-2*x^3)*exp(4)-2*x^2+2*x)*log(x)+2*x^4-2*x^3)*log(x^2-x)+(x^2-x)*exp(4)^2
*log(x)^2+(2*x^2-2*x)*exp(4)*log(x)+x^2-x),x, algorithm="fricas")

[Out]

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

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giac [F(-1)]  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^2-x)*log(x)^2+(-2*x^4+2*x^3)*log(x)+x^6-x^5)*log(x^2-x)^2+((-2*x^2+2*x)*exp(4)*log(x)^2+((2*x^4
-2*x^3)*exp(4)-2*x^2+2*x)*log(x)+2*x^4+2*x^3-4*x^2-2*x+2)*log(x^2-x)+(x^2-x)*exp(4)^2*log(x)^2+((2*x^2-2*x)*ex
p(4)-4*x+2)*log(x)+(2*x-2)*exp(4)+4*x^3-x^2-x)/(((x^2-x)*log(x)^2+(-2*x^4+2*x^3)*log(x)+x^6-x^5)*log(x^2-x)^2+
((-2*x^2+2*x)*exp(4)*log(x)^2+((2*x^4-2*x^3)*exp(4)-2*x^2+2*x)*log(x)+2*x^4-2*x^3)*log(x^2-x)+(x^2-x)*exp(4)^2
*log(x)^2+(2*x^2-2*x)*exp(4)*log(x)+x^2-x),x, algorithm="giac")

[Out]

Timed out

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maple [C]  time = 0.37, size = 216, normalized size = 6.75

method	result	size
risch	\(x -\frac {4 i}{\pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )-\pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}-\pi \,x^{2} \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}+\pi \,x^{2} \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}-\ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )+\ln \relax (x ) \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}+\ln \relax (x ) \pi \,\mathrm {csgn}\left (i \left (x -1\right )\right ) \mathrm {csgn}\left (i x \left (x -1\right )\right )^{2}-\ln \relax (x ) \pi \mathrm {csgn}\left (i x \left (x -1\right )\right )^{3}+2 i x^{2} \ln \relax (x )+2 i x^{2} \ln \left (x -1\right )+2 i {\mathrm e}^{4} \ln \relax (x )-2 i \ln \relax (x )^{2}-2 i \ln \relax (x ) \ln \left (x -1\right )+2 i}\)	\(216\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^2-x)*ln(x)^2+(-2*x^4+2*x^3)*ln(x)+x^6-x^5)*ln(x^2-x)^2+((-2*x^2+2*x)*exp(4)*ln(x)^2+((2*x^4-2*x^3)*ex
p(4)-2*x^2+2*x)*ln(x)+2*x^4+2*x^3-4*x^2-2*x+2)*ln(x^2-x)+(x^2-x)*exp(4)^2*ln(x)^2+((2*x^2-2*x)*exp(4)-4*x+2)*l
n(x)+(2*x-2)*exp(4)+4*x^3-x^2-x)/(((x^2-x)*ln(x)^2+(-2*x^4+2*x^3)*ln(x)+x^6-x^5)*ln(x^2-x)^2+((-2*x^2+2*x)*exp
(4)*ln(x)^2+((2*x^4-2*x^3)*exp(4)-2*x^2+2*x)*ln(x)+2*x^4-2*x^3)*ln(x^2-x)+(x^2-x)*exp(4)^2*ln(x)^2+(2*x^2-2*x)
*exp(4)*ln(x)+x^2-x),x,method=_RETURNVERBOSE)

[Out]

x-4*I/(Pi*x^2*csgn(I*x)*csgn(I*(x-1))*csgn(I*x*(x-1))-Pi*x^2*csgn(I*x)*csgn(I*x*(x-1))^2-Pi*x^2*csgn(I*(x-1))*
csgn(I*x*(x-1))^2+Pi*x^2*csgn(I*x*(x-1))^3-ln(x)*Pi*csgn(I*x)*csgn(I*(x-1))*csgn(I*x*(x-1))+ln(x)*Pi*csgn(I*x)
*csgn(I*x*(x-1))^2+ln(x)*Pi*csgn(I*(x-1))*csgn(I*x*(x-1))^2-ln(x)*Pi*csgn(I*x*(x-1))^3+2*I*x^2*ln(x)+2*I*x^2*l
n(x-1)+2*I*exp(4)*ln(x)-2*I*ln(x)^2-2*I*ln(x)*ln(x-1)+2*I)

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maxima [B]  time = 0.57, size = 72, normalized size = 2.25 \begin {gather*} -\frac {x \log \relax (x)^{2} - {\left (x^{3} - x \log \relax (x)\right )} \log \left (x - 1\right ) - {\left (x^{3} + x e^{4}\right )} \log \relax (x) - x + 2}{{\left (x^{2} - \log \relax (x)\right )} \log \left (x - 1\right ) + {\left (x^{2} + e^{4}\right )} \log \relax (x) - \log \relax (x)^{2} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-x)*log(x)^2+(-2*x^4+2*x^3)*log(x)+x^6-x^5)*log(x^2-x)^2+((-2*x^2+2*x)*exp(4)*log(x)^2+((2*x^4
-2*x^3)*exp(4)-2*x^2+2*x)*log(x)+2*x^4+2*x^3-4*x^2-2*x+2)*log(x^2-x)+(x^2-x)*exp(4)^2*log(x)^2+((2*x^2-2*x)*ex
p(4)-4*x+2)*log(x)+(2*x-2)*exp(4)+4*x^3-x^2-x)/(((x^2-x)*log(x)^2+(-2*x^4+2*x^3)*log(x)+x^6-x^5)*log(x^2-x)^2+
((-2*x^2+2*x)*exp(4)*log(x)^2+((2*x^4-2*x^3)*exp(4)-2*x^2+2*x)*log(x)+2*x^4-2*x^3)*log(x^2-x)+(x^2-x)*exp(4)^2
*log(x)^2+(2*x^2-2*x)*exp(4)*log(x)+x^2-x),x, algorithm="maxima")

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {x-{\ln \left (x^2-x\right )}^2\,\left (\ln \relax (x)\,\left (2\,x^3-2\,x^4\right )-{\ln \relax (x)}^2\,\left (x-x^2\right )-x^5+x^6\right )-\ln \left (x^2-x\right )\,\left (2\,x^3-\ln \relax (x)\,\left ({\mathrm {e}}^4\,\left (2\,x^3-2\,x^4\right )-2\,x+2\,x^2\right )-4\,x^2-2\,x+2\,x^4+{\mathrm {e}}^4\,{\ln \relax (x)}^2\,\left (2\,x-2\,x^2\right )+2\right )+\ln \relax (x)\,\left (4\,x+{\mathrm {e}}^4\,\left (2\,x-2\,x^2\right )-2\right )+x^2-4\,x^3-{\mathrm {e}}^4\,\left (2\,x-2\right )+{\mathrm {e}}^8\,{\ln \relax (x)}^2\,\left (x-x^2\right )}{x+\ln \left (x^2-x\right )\,\left (\ln \relax (x)\,\left ({\mathrm {e}}^4\,\left (2\,x^3-2\,x^4\right )-2\,x+2\,x^2\right )+2\,x^3-2\,x^4-{\mathrm {e}}^4\,{\ln \relax (x)}^2\,\left (2\,x-2\,x^2\right )\right )-{\ln \left (x^2-x\right )}^2\,\left (\ln \relax (x)\,\left (2\,x^3-2\,x^4\right )-{\ln \relax (x)}^2\,\left (x-x^2\right )-x^5+x^6\right )-x^2+{\mathrm {e}}^4\,\ln \relax (x)\,\left (2\,x-2\,x^2\right )+{\mathrm {e}}^8\,{\ln \relax (x)}^2\,\left (x-x^2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x - log(x^2 - x)^2*(log(x)*(2*x^3 - 2*x^4) - log(x)^2*(x - x^2) - x^5 + x^6) - log(x^2 - x)*(2*x^3 - log(
x)*(exp(4)*(2*x^3 - 2*x^4) - 2*x + 2*x^2) - 4*x^2 - 2*x + 2*x^4 + exp(4)*log(x)^2*(2*x - 2*x^2) + 2) + log(x)*
(4*x + exp(4)*(2*x - 2*x^2) - 2) + x^2 - 4*x^3 - exp(4)*(2*x - 2) + exp(8)*log(x)^2*(x - x^2))/(x + log(x^2 -
x)*(log(x)*(exp(4)*(2*x^3 - 2*x^4) - 2*x + 2*x^2) + 2*x^3 - 2*x^4 - exp(4)*log(x)^2*(2*x - 2*x^2)) - log(x^2 -
x)^2*(log(x)*(2*x^3 - 2*x^4) - log(x)^2*(x - x^2) - x^5 + x^6) - x^2 + exp(4)*log(x)*(2*x - 2*x^2) + exp(8)*l
og(x)^2*(x - x^2)),x)

[Out]

int((x - log(x^2 - x)^2*(log(x)*(2*x^3 - 2*x^4) - log(x)^2*(x - x^2) - x^5 + x^6) - log(x^2 - x)*(2*x^3 - log(
x)*(exp(4)*(2*x^3 - 2*x^4) - 2*x + 2*x^2) - 4*x^2 - 2*x + 2*x^4 + exp(4)*log(x)^2*(2*x - 2*x^2) + 2) + log(x)*
(4*x + exp(4)*(2*x - 2*x^2) - 2) + x^2 - 4*x^3 - exp(4)*(2*x - 2) + exp(8)*log(x)^2*(x - x^2))/(x + log(x^2 -
x)*(log(x)*(exp(4)*(2*x^3 - 2*x^4) - 2*x + 2*x^2) + 2*x^3 - 2*x^4 - exp(4)*log(x)^2*(2*x - 2*x^2)) - log(x^2 -
x)^2*(log(x)*(2*x^3 - 2*x^4) - log(x)^2*(x - x^2) - x^5 + x^6) - x^2 + exp(4)*log(x)*(2*x - 2*x^2) + exp(8)*l
og(x)^2*(x - x^2)), x)

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sympy [A]  time = 1.00, size = 24, normalized size = 0.75 \begin {gather*} x - \frac {2}{\left (x^{2} - \log {\relax (x )}\right ) \log {\left (x^{2} - x \right )} + e^{4} \log {\relax (x )} + 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**2-x)*ln(x)**2+(-2*x**4+2*x**3)*ln(x)+x**6-x**5)*ln(x**2-x)**2+((-2*x**2+2*x)*exp(4)*ln(x)**2+(
(2*x**4-2*x**3)*exp(4)-2*x**2+2*x)*ln(x)+2*x**4+2*x**3-4*x**2-2*x+2)*ln(x**2-x)+(x**2-x)*exp(4)**2*ln(x)**2+((
2*x**2-2*x)*exp(4)-4*x+2)*ln(x)+(2*x-2)*exp(4)+4*x**3-x**2-x)/(((x**2-x)*ln(x)**2+(-2*x**4+2*x**3)*ln(x)+x**6-
x**5)*ln(x**2-x)**2+((-2*x**2+2*x)*exp(4)*ln(x)**2+((2*x**4-2*x**3)*exp(4)-2*x**2+2*x)*ln(x)+2*x**4-2*x**3)*ln
(x**2-x)+(x**2-x)*exp(4)**2*ln(x)**2+(2*x**2-2*x)*exp(4)*ln(x)+x**2-x),x)

[Out]

x - 2/((x**2 - log(x))*log(x**2 - x) + exp(4)*log(x) + 1)

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