\(\int \frac {(e^{x^2} (-2+4 x)+(-2+4 x) \log (4)) \log (x-x^2)+(e^{x^2} (-1+x-2 x^2+2 x^3)+(-1+x) \log (4)) \log ^2(x-x^2)}{-10+10 x+(-1+x) \log (3)} \, dx\) [1511]

Optimal result

Integrand size = 81, antiderivative size = 26 \[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\frac {x \left (e^{x^2}+\log (4)\right ) \log ^2\left (x-x^2\right )}{10+\log (3)} \]

[Out]

x*(2*ln(2)+exp(x^2))*ln(-x^2+x)^2/(10+ln(3))

Rubi [F]

\[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx \]

[In]

Int[((E^x^2*(-2 + 4*x) + (-2 + 4*x)*Log[4])*Log[x - x^2] + (E^x^2*(-1 + x - 2*x^2 + 2*x^3) + (-1 + x)*Log[4])*
Log[x - x^2]^2)/(-10 + 10*x + (-1 + x)*Log[3]),x]

[Out]

(-4*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, x^2])/(10 + Log[3]) - (4*(1 - x)*Log[4]*Log[1 - x])/(10 + Log[
3]) + (Log[4]*Log[1 - x]^2)/(10 + Log[3]) - (4*Log[4]*Log[x])/(10 + Log[3]) + (4*x*Log[4]*Log[x])/(10 + Log[3]
) - (Log[4]*Log[x]^2)/(10 + Log[3]) - (4*x*Log[4]*(Log[1 - x] + Log[x] - Log[(1 - x)*x]))/(10 + Log[3]) - (2*L
og[4]*Log[1 - x]*(Log[1 - x] + Log[x] - Log[(1 - x)*x]))/(10 + Log[3]) + (2*Sqrt[Pi]*Erfi[x]*Log[(1 - x)*x])/(
10 + Log[3]) + (4*(1 - x)*Log[4]*Log[(1 - x)*x])/(10 + Log[3]) + (2*Log[4]*Log[x]*Log[(1 - x)*x])/(10 + Log[3]
) - ((1 - x)*Log[4]*Log[(1 - x)*x]^2)/(10 + Log[3]) + (2*Log[(1 - x)*x]*Defer[Int][E^x^2/(-1 + x), x])/(10 + L
og[3]) - (2*Sqrt[Pi]*Defer[Int][Erfi[x]/(-1 + x), x])/(10 + Log[3]) + Defer[Int][E^x^2*Log[(1 - x)*x]^2, x]/(1
0 + Log[3]) + (2*Defer[Int][E^x^2*x^2*Log[(1 - x)*x]^2, x])/(10 + Log[3]) - (2*Defer[Int][Defer[Int][E^x^2/(-1
+ x), x]/(-1 + x), x])/(10 + Log[3]) - (2*Defer[Int][Defer[Int][E^x^2/(-1 + x), x]/x, x])/(10 + Log[3])

Rubi steps \begin{align*} \text {integral}& = \int \frac {-\left (\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )\right )-\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{10+\log (3)-x (10+\log (3))} \, dx \\ & = \int \left (\frac {\log (4) \log ((1-x) x) (2-4 x+\log (-((-1+x) x))-x \log (-((-1+x) x)))}{(1-x) (10+\log (3))}+\frac {e^{x^2} \log ((1-x) x) \left (2-4 x+\log (-((-1+x) x))-x \log (-((-1+x) x))+2 x^2 \log (-((-1+x) x))-2 x^3 \log (-((-1+x) x))\right )}{(1-x) (10+\log (3))}\right ) \, dx \\ & = \frac {\int \frac {e^{x^2} \log ((1-x) x) \left (2-4 x+\log (-((-1+x) x))-x \log (-((-1+x) x))+2 x^2 \log (-((-1+x) x))-2 x^3 \log (-((-1+x) x))\right )}{1-x} \, dx}{10+\log (3)}+\frac {\log (4) \int \frac {\log ((1-x) x) (2-4 x+\log (-((-1+x) x))-x \log (-((-1+x) x)))}{1-x} \, dx}{10+\log (3)} \\ & = \frac {\int \frac {e^{x^2} \log ((1-x) x) \left (2-4 x-\left (-1+x-2 x^2+2 x^3\right ) \log (-((-1+x) x))\right )}{1-x} \, dx}{10+\log (3)}+\frac {\log (4) \int \left (\frac {2 (1-2 x) \log ((1-x) x)}{1-x}+\log ^2((1-x) x)\right ) \, dx}{10+\log (3)} \\ & = \frac {\int \left (\frac {2 e^{x^2} (1-2 x) \log ((1-x) x)}{1-x}+e^{x^2} \left (1+2 x^2\right ) \log ^2((1-x) x)\right ) \, dx}{10+\log (3)}+\frac {\log (4) \int \log ^2((1-x) x) \, dx}{10+\log (3)}+\frac {(2 \log (4)) \int \frac {(1-2 x) \log ((1-x) x)}{1-x} \, dx}{10+\log (3)} \\ & = -\frac {(1-x) \log (4) \log ^2((1-x) x)}{10+\log (3)}+\frac {\int e^{x^2} \left (1+2 x^2\right ) \log ^2((1-x) x) \, dx}{10+\log (3)}+\frac {2 \int \frac {e^{x^2} (1-2 x) \log ((1-x) x)}{1-x} \, dx}{10+\log (3)}+\frac {(2 \log (4)) \int \frac {(1-2 x) \log (1-x)}{1-x} \, dx}{10+\log (3)}+\frac {(2 \log (4)) \int \frac {(1-2 x) \log (x)}{1-x} \, dx}{10+\log (3)}+\frac {(2 \log (4)) \int \frac {\log ((1-x) x)}{x} \, dx}{10+\log (3)}-\frac {(4 \log (4)) \int \log ((1-x) x) \, dx}{10+\log (3)}-\frac {(2 \log (4) (\log (1-x)+\log (x)-\log ((1-x) x))) \int \frac {1-2 x}{1-x} \, dx}{10+\log (3)} \\ & = \frac {2 \sqrt {\pi } \text {erfi}(x) \log ((1-x) x)}{10+\log (3)}+\frac {4 (1-x) \log (4) \log ((1-x) x)}{10+\log (3)}+\frac {2 \log (4) \log (x) \log ((1-x) x)}{10+\log (3)}-\frac {(1-x) \log (4) \log ^2((1-x) x)}{10+\log (3)}+\frac {\int \left (e^{x^2} \log ^2((1-x) x)+2 e^{x^2} x^2 \log ^2((1-x) x)\right ) \, dx}{10+\log (3)}-\frac {2 \int \frac {(1-2 x) \left (\sqrt {\pi } \text {erfi}(x)+\int \frac {e^{x^2}}{-1+x} \, dx\right )}{(1-x) x} \, dx}{10+\log (3)}+\frac {(2 \log (4)) \int \frac {\log (x)}{1-x} \, dx}{10+\log (3)}-\frac {(2 \log (4)) \int \frac {\log (x)}{x} \, dx}{10+\log (3)}+\frac {(2 \log (4)) \int \left (2 \log (x)+\frac {\log (x)}{-1+x}\right ) \, dx}{10+\log (3)}-\frac {(2 \log (4)) \text {Subst}\left (\int \frac {(-1+2 x) \log (x)}{x} \, dx,x,1-x\right )}{10+\log (3)}-\frac {(4 \log (4)) \int \frac {1}{x} \, dx}{10+\log (3)}+\frac {(8 \log (4)) \int 1 \, dx}{10+\log (3)}-\frac {(2 \log (4) (\log (1-x)+\log (x)-\log ((1-x) x))) \int \left (2+\frac {1}{-1+x}\right ) \, dx}{10+\log (3)}+\frac {(2 \log ((1-x) x)) \int \frac {e^{x^2}}{-1+x} \, dx}{10+\log (3)} \\ & = \frac {8 x \log (4)}{10+\log (3)}-\frac {4 \log (4) \log (x)}{10+\log (3)}-\frac {\log (4) \log ^2(x)}{10+\log (3)}-\frac {4 x \log (4) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}-\frac {2 \log (4) \log (1-x) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}+\frac {2 \sqrt {\pi } \text {erfi}(x) \log ((1-x) x)}{10+\log (3)}+\frac {4 (1-x) \log (4) \log ((1-x) x)}{10+\log (3)}+\frac {2 \log (4) \log (x) \log ((1-x) x)}{10+\log (3)}-\frac {(1-x) \log (4) \log ^2((1-x) x)}{10+\log (3)}+\frac {2 \log (4) \operatorname {PolyLog}(2,1-x)}{10+\log (3)}+\frac {\int e^{x^2} \log ^2((1-x) x) \, dx}{10+\log (3)}+\frac {2 \int e^{x^2} x^2 \log ^2((1-x) x) \, dx}{10+\log (3)}-\frac {2 \int \left (\frac {\sqrt {\pi } (-1+2 x) \text {erfi}(x)}{(-1+x) x}+\frac {(-1+2 x) \int \frac {e^{x^2}}{-1+x} \, dx}{(-1+x) x}\right ) \, dx}{10+\log (3)}+\frac {(2 \log (4)) \int \frac {\log (x)}{-1+x} \, dx}{10+\log (3)}+\frac {(2 \log (4)) \text {Subst}\left (\int \frac {\log (x)}{x} \, dx,x,1-x\right )}{10+\log (3)}+\frac {(4 \log (4)) \int \log (x) \, dx}{10+\log (3)}-\frac {(4 \log (4)) \text {Subst}(\int \log (x) \, dx,x,1-x)}{10+\log (3)}+\frac {(2 \log ((1-x) x)) \int \frac {e^{x^2}}{-1+x} \, dx}{10+\log (3)} \\ & = -\frac {4 (1-x) \log (4) \log (1-x)}{10+\log (3)}+\frac {\log (4) \log ^2(1-x)}{10+\log (3)}-\frac {4 \log (4) \log (x)}{10+\log (3)}+\frac {4 x \log (4) \log (x)}{10+\log (3)}-\frac {\log (4) \log ^2(x)}{10+\log (3)}-\frac {4 x \log (4) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}-\frac {2 \log (4) \log (1-x) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}+\frac {2 \sqrt {\pi } \text {erfi}(x) \log ((1-x) x)}{10+\log (3)}+\frac {4 (1-x) \log (4) \log ((1-x) x)}{10+\log (3)}+\frac {2 \log (4) \log (x) \log ((1-x) x)}{10+\log (3)}-\frac {(1-x) \log (4) \log ^2((1-x) x)}{10+\log (3)}+\frac {\int e^{x^2} \log ^2((1-x) x) \, dx}{10+\log (3)}+\frac {2 \int e^{x^2} x^2 \log ^2((1-x) x) \, dx}{10+\log (3)}-\frac {2 \int \frac {(-1+2 x) \int \frac {e^{x^2}}{-1+x} \, dx}{(-1+x) x} \, dx}{10+\log (3)}-\frac {\left (2 \sqrt {\pi }\right ) \int \frac {(-1+2 x) \text {erfi}(x)}{(-1+x) x} \, dx}{10+\log (3)}+\frac {(2 \log ((1-x) x)) \int \frac {e^{x^2}}{-1+x} \, dx}{10+\log (3)} \\ & = -\frac {4 (1-x) \log (4) \log (1-x)}{10+\log (3)}+\frac {\log (4) \log ^2(1-x)}{10+\log (3)}-\frac {4 \log (4) \log (x)}{10+\log (3)}+\frac {4 x \log (4) \log (x)}{10+\log (3)}-\frac {\log (4) \log ^2(x)}{10+\log (3)}-\frac {4 x \log (4) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}-\frac {2 \log (4) \log (1-x) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}+\frac {2 \sqrt {\pi } \text {erfi}(x) \log ((1-x) x)}{10+\log (3)}+\frac {4 (1-x) \log (4) \log ((1-x) x)}{10+\log (3)}+\frac {2 \log (4) \log (x) \log ((1-x) x)}{10+\log (3)}-\frac {(1-x) \log (4) \log ^2((1-x) x)}{10+\log (3)}+\frac {\int e^{x^2} \log ^2((1-x) x) \, dx}{10+\log (3)}+\frac {2 \int e^{x^2} x^2 \log ^2((1-x) x) \, dx}{10+\log (3)}-\frac {2 \int \left (\frac {\int \frac {e^{x^2}}{-1+x} \, dx}{-1+x}+\frac {\int \frac {e^{x^2}}{-1+x} \, dx}{x}\right ) \, dx}{10+\log (3)}-\frac {\left (2 \sqrt {\pi }\right ) \int \left (\frac {\text {erfi}(x)}{-1+x}+\frac {\text {erfi}(x)}{x}\right ) \, dx}{10+\log (3)}+\frac {(2 \log ((1-x) x)) \int \frac {e^{x^2}}{-1+x} \, dx}{10+\log (3)} \\ & = -\frac {4 (1-x) \log (4) \log (1-x)}{10+\log (3)}+\frac {\log (4) \log ^2(1-x)}{10+\log (3)}-\frac {4 \log (4) \log (x)}{10+\log (3)}+\frac {4 x \log (4) \log (x)}{10+\log (3)}-\frac {\log (4) \log ^2(x)}{10+\log (3)}-\frac {4 x \log (4) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}-\frac {2 \log (4) \log (1-x) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}+\frac {2 \sqrt {\pi } \text {erfi}(x) \log ((1-x) x)}{10+\log (3)}+\frac {4 (1-x) \log (4) \log ((1-x) x)}{10+\log (3)}+\frac {2 \log (4) \log (x) \log ((1-x) x)}{10+\log (3)}-\frac {(1-x) \log (4) \log ^2((1-x) x)}{10+\log (3)}+\frac {\int e^{x^2} \log ^2((1-x) x) \, dx}{10+\log (3)}+\frac {2 \int e^{x^2} x^2 \log ^2((1-x) x) \, dx}{10+\log (3)}-\frac {2 \int \frac {\int \frac {e^{x^2}}{-1+x} \, dx}{-1+x} \, dx}{10+\log (3)}-\frac {2 \int \frac {\int \frac {e^{x^2}}{-1+x} \, dx}{x} \, dx}{10+\log (3)}-\frac {\left (2 \sqrt {\pi }\right ) \int \frac {\text {erfi}(x)}{-1+x} \, dx}{10+\log (3)}-\frac {\left (2 \sqrt {\pi }\right ) \int \frac {\text {erfi}(x)}{x} \, dx}{10+\log (3)}+\frac {(2 \log ((1-x) x)) \int \frac {e^{x^2}}{-1+x} \, dx}{10+\log (3)} \\ & = -\frac {4 x \, _2F_2\left (\frac {1}{2},\frac {1}{2};\frac {3}{2},\frac {3}{2};x^2\right )}{10+\log (3)}-\frac {4 (1-x) \log (4) \log (1-x)}{10+\log (3)}+\frac {\log (4) \log ^2(1-x)}{10+\log (3)}-\frac {4 \log (4) \log (x)}{10+\log (3)}+\frac {4 x \log (4) \log (x)}{10+\log (3)}-\frac {\log (4) \log ^2(x)}{10+\log (3)}-\frac {4 x \log (4) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}-\frac {2 \log (4) \log (1-x) (\log (1-x)+\log (x)-\log ((1-x) x))}{10+\log (3)}+\frac {2 \sqrt {\pi } \text {erfi}(x) \log ((1-x) x)}{10+\log (3)}+\frac {4 (1-x) \log (4) \log ((1-x) x)}{10+\log (3)}+\frac {2 \log (4) \log (x) \log ((1-x) x)}{10+\log (3)}-\frac {(1-x) \log (4) \log ^2((1-x) x)}{10+\log (3)}+\frac {\int e^{x^2} \log ^2((1-x) x) \, dx}{10+\log (3)}+\frac {2 \int e^{x^2} x^2 \log ^2((1-x) x) \, dx}{10+\log (3)}-\frac {2 \int \frac {\int \frac {e^{x^2}}{-1+x} \, dx}{-1+x} \, dx}{10+\log (3)}-\frac {2 \int \frac {\int \frac {e^{x^2}}{-1+x} \, dx}{x} \, dx}{10+\log (3)}-\frac {\left (2 \sqrt {\pi }\right ) \int \frac {\text {erfi}(x)}{-1+x} \, dx}{10+\log (3)}+\frac {(2 \log ((1-x) x)) \int \frac {e^{x^2}}{-1+x} \, dx}{10+\log (3)} \\ \end{align*}

Mathematica [F]

\[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx \]

[In]

Integrate[((E^x^2*(-2 + 4*x) + (-2 + 4*x)*Log[4])*Log[x - x^2] + (E^x^2*(-1 + x - 2*x^2 + 2*x^3) + (-1 + x)*Lo
g[4])*Log[x - x^2]^2)/(-10 + 10*x + (-1 + x)*Log[3]),x]

[Out]

Integrate[((E^x^2*(-2 + 4*x) + (-2 + 4*x)*Log[4])*Log[x - x^2] + (E^x^2*(-1 + x - 2*x^2 + 2*x^3) + (-1 + x)*Lo
g[4])*Log[x - x^2]^2)/(-10 + 10*x + (-1 + x)*Log[3]), x]

Maple [A] (verified)

Time = 1.04 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.54

method	result	size
parallelrisch	\(\frac {2 \ln \left (2\right ) \ln \left (-x^{2}+x \right )^{2} x +{\mathrm e}^{x^{2}} \ln \left (-x^{2}+x \right )^{2} x}{10+\ln \left (3\right )}\)	\(40\)
risch	\(\text {Expression too large to display}\)	\(1460\)

[In]

int((((2*x^3-2*x^2+x-1)*exp(x^2)+2*(-1+x)*ln(2))*ln(-x^2+x)^2+((4*x-2)*exp(x^2)+2*(4*x-2)*ln(2))*ln(-x^2+x))/(
(-1+x)*ln(3)+10*x-10),x,method=_RETURNVERBOSE)

[Out]

(2*ln(2)*ln(-x^2+x)^2*x+exp(x^2)*ln(-x^2+x)^2*x)/(10+ln(3))

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\frac {{\left (x e^{\left (x^{2}\right )} + 2 \, x \log \left (2\right )\right )} \log \left (-x^{2} + x\right )^{2}}{\log \left (3\right ) + 10} \]

[In]

integrate((((2*x^3-2*x^2+x-1)*exp(x^2)+2*(-1+x)*log(2))*log(-x^2+x)^2+((4*x-2)*exp(x^2)+2*(4*x-2)*log(2))*log(
-x^2+x))/((-1+x)*log(3)+10*x-10),x, algorithm="fricas")

[Out]

(x*e^(x^2) + 2*x*log(2))*log(-x^2 + x)^2/(log(3) + 10)

Sympy [F(-1)]

Timed out. \[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\text {Timed out} \]

[In]

integrate((((2*x**3-2*x**2+x-1)*exp(x**2)+2*(-1+x)*ln(2))*ln(-x**2+x)**2+((4*x-2)*exp(x**2)+2*(4*x-2)*ln(2))*l
n(-x**2+x))/((-1+x)*ln(3)+10*x-10),x)

[Out]

Timed out

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 72 vs. \(2 (27) = 54\).

Time = 0.32 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.77 \[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\frac {x e^{\left (x^{2}\right )} \log \left (x\right )^{2} + 2 \, x \log \left (2\right ) \log \left (x\right )^{2} + {\left (x e^{\left (x^{2}\right )} + 2 \, x \log \left (2\right )\right )} \log \left (-x + 1\right )^{2} + 2 \, {\left (x e^{\left (x^{2}\right )} \log \left (x\right ) + 2 \, x \log \left (2\right ) \log \left (x\right )\right )} \log \left (-x + 1\right )}{\log \left (3\right ) + 10} \]

[In]

integrate((((2*x^3-2*x^2+x-1)*exp(x^2)+2*(-1+x)*log(2))*log(-x^2+x)^2+((4*x-2)*exp(x^2)+2*(4*x-2)*log(2))*log(
-x^2+x))/((-1+x)*log(3)+10*x-10),x, algorithm="maxima")

[Out]

(x*e^(x^2)*log(x)^2 + 2*x*log(2)*log(x)^2 + (x*e^(x^2) + 2*x*log(2))*log(-x + 1)^2 + 2*(x*e^(x^2)*log(x) + 2*x
*log(2)*log(x))*log(-x + 1))/(log(3) + 10)

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.50 \[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\frac {x e^{\left (x^{2}\right )} \log \left (-x^{2} + x\right )^{2} + 2 \, x \log \left (2\right ) \log \left (-x^{2} + x\right )^{2}}{\log \left (3\right ) + 10} \]

[In]

integrate((((2*x^3-2*x^2+x-1)*exp(x^2)+2*(-1+x)*log(2))*log(-x^2+x)^2+((4*x-2)*exp(x^2)+2*(4*x-2)*log(2))*log(
-x^2+x))/((-1+x)*log(3)+10*x-10),x, algorithm="giac")

[Out]

(x*e^(x^2)*log(-x^2 + x)^2 + 2*x*log(2)*log(-x^2 + x)^2)/(log(3) + 10)

Mupad [F(-1)]

Timed out. \[ \int \frac {\left (e^{x^2} (-2+4 x)+(-2+4 x) \log (4)\right ) \log \left (x-x^2\right )+\left (e^{x^2} \left (-1+x-2 x^2+2 x^3\right )+(-1+x) \log (4)\right ) \log ^2\left (x-x^2\right )}{-10+10 x+(-1+x) \log (3)} \, dx=\int \frac {\left (2\,\ln \left (2\right )\,\left (x-1\right )+{\mathrm {e}}^{x^2}\,\left (2\,x^3-2\,x^2+x-1\right )\right )\,{\ln \left (x-x^2\right )}^2+\left (2\,\ln \left (2\right )\,\left (4\,x-2\right )+{\mathrm {e}}^{x^2}\,\left (4\,x-2\right )\right )\,\ln \left (x-x^2\right )}{10\,x+\ln \left (3\right )\,\left (x-1\right )-10} \,d x \]

[In]

int((log(x - x^2)*(2*log(2)*(4*x - 2) + exp(x^2)*(4*x - 2)) + log(x - x^2)^2*(2*log(2)*(x - 1) + exp(x^2)*(x -
2*x^2 + 2*x^3 - 1)))/(10*x + log(3)*(x - 1) - 10),x)

[Out]

int((log(x - x^2)*(2*log(2)*(4*x - 2) + exp(x^2)*(4*x - 2)) + log(x - x^2)^2*(2*log(2)*(x - 1) + exp(x^2)*(x -
2*x^2 + 2*x^3 - 1)))/(10*x + log(3)*(x - 1) - 10), x)