3.20.51 \(\int \frac {2 x^3-4 x^4+(6 x-12 x^2-4 x^3+3 x^4+x^5) \log (-x+x^2)+(-12 x+6 x^2+6 x^3) \log ^2(-x+x^2)+(-10+9 x+x^2) \log ^3(-x+x^2)}{(-x^4+x^5) \log (-x+x^2)+(-6 x^2+6 x^3) \log ^2(-x+x^2)+(-9+8 x+x^2) \log ^3(-x+x^2)} \, dx\)

Optimal. Leaf size=25 \[ x+\log \left (4 \left (x+\left (3+\frac {x^2}{\log \left (-x+x^2\right )}\right )^2\right )\right ) \]

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Rubi [F]  time = 15.01, 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 {2 x^3-4 x^4+\left (6 x-12 x^2-4 x^3+3 x^4+x^5\right ) \log \left (-x+x^2\right )+\left (-12 x+6 x^2+6 x^3\right ) \log ^2\left (-x+x^2\right )+\left (-10+9 x+x^2\right ) \log ^3\left (-x+x^2\right )}{\left (-x^4+x^5\right ) \log \left (-x+x^2\right )+\left (-6 x^2+6 x^3\right ) \log ^2\left (-x+x^2\right )+\left (-9+8 x+x^2\right ) \log ^3\left (-x+x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(2*x^3 - 4*x^4 + (6*x - 12*x^2 - 4*x^3 + 3*x^4 + x^5)*Log[-x + x^2] + (-12*x + 6*x^2 + 6*x^3)*Log[-x + x^2
]^2 + (-10 + 9*x + x^2)*Log[-x + x^2]^3)/((-x^4 + x^5)*Log[-x + x^2] + (-6*x^2 + 6*x^3)*Log[-x + x^2]^2 + (-9
+ 8*x + x^2)*Log[-x + x^2]^3),x]

[Out]

x + Log[9 + x] - 2*Defer[Int][(-1 + 2*x)/((-1 + x)*x*Log[(-1 + x)*x]), x] + 735*Defer[Int][(x^4 + 6*x^2*Log[(-
1 + x)*x] + 9*Log[(-1 + x)*x]^2 + x*Log[(-1 + x)*x]^2)^(-1), x] + 6*Defer[Int][1/((-1 + x)*(x^4 + 6*x^2*Log[(-
1 + x)*x] + 9*Log[(-1 + x)*x]^2 + x*Log[(-1 + x)*x]^2)), x] - 69*Defer[Int][x/(x^4 + 6*x^2*Log[(-1 + x)*x] + 9
*Log[(-1 + x)*x]^2 + x*Log[(-1 + x)*x]^2), x] + 9*Defer[Int][x^2/(x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log[(-1 + x)
*x]^2 + x*Log[(-1 + x)*x]^2), x] + 3*Defer[Int][x^3/(x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log[(-1 + x)*x]^2 + x*Log
[(-1 + x)*x]^2), x] - 6561*Defer[Int][1/((9 + x)*(x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log[(-1 + x)*x]^2 + x*Log[(-
1 + x)*x]^2)), x] + 58*Defer[Int][Log[(-1 + x)*x]/(x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log[(-1 + x)*x]^2 + x*Log[(
-1 + x)*x]^2), x] + 20*Defer[Int][Log[(-1 + x)*x]/((-1 + x)*(x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log[(-1 + x)*x]^2
+ x*Log[(-1 + x)*x]^2)), x] + 6*Defer[Int][(x*Log[(-1 + x)*x])/(x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log[(-1 + x)*
x]^2 + x*Log[(-1 + x)*x]^2), x] - 486*Defer[Int][Log[(-1 + x)*x]/((9 + x)*(x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log
[(-1 + x)*x]^2 + x*Log[(-1 + x)*x]^2)), x] + 18*Defer[Int][Log[(-1 + x)*x]/(x^5 + 6*x^3*Log[(-1 + x)*x] + x*(9
+ x)*Log[(-1 + x)*x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-2 x^3+4 x^4-\left (6 x-12 x^2-4 x^3+3 x^4+x^5\right ) \log \left (-x+x^2\right )-\left (-12 x+6 x^2+6 x^3\right ) \log ^2\left (-x+x^2\right )-\left (-10+9 x+x^2\right ) \log ^3\left (-x+x^2\right )}{(1-x) \log ((-1+x) x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx\\ &=\int \left (\frac {x \left (6-12 x-4 x^2+3 x^3+x^4\right )}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}-\frac {2 x^3 (-1+2 x)}{(-1+x) \log ((-1+x) x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}+\frac {6 x (2+x) \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}+\frac {(10+x) \log ^2((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}\right ) \, dx\\ &=-\left (2 \int \frac {x^3 (-1+2 x)}{(-1+x) \log ((-1+x) x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx\right )+6 \int \frac {x (2+x) \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx+\int \frac {x \left (6-12 x-4 x^2+3 x^3+x^4\right )}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+\int \frac {(10+x) \log ^2((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx\\ &=-\left (2 \int \left (\frac {-1+2 x}{(-1+x) x \log ((-1+x) x)}-\frac {(-1+2 x) \left (6 x^2+9 \log ((-1+x) x)+x \log ((-1+x) x)\right )}{(-1+x) x \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}\right ) \, dx\right )+6 \int \left (\frac {2 x \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}+\frac {x^2 \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}\right ) \, dx+\int \left (-\frac {6}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}-\frac {6}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}-\frac {12 x}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}+\frac {4 x^3}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}+\frac {x^4}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}\right ) \, dx+\int \left (\frac {10+x}{9+x}-\frac {x^2 (10+x) \left (x^2+6 \log ((-1+x) x)\right )}{(9+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}\right ) \, dx\\ &=-\left (2 \int \frac {-1+2 x}{(-1+x) x \log ((-1+x) x)} \, dx\right )+2 \int \frac {(-1+2 x) \left (6 x^2+9 \log ((-1+x) x)+x \log ((-1+x) x)\right )}{(-1+x) x \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+4 \int \frac {x^3}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-6 \int \frac {1}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-6 \int \frac {1}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+6 \int \frac {x^2 \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-12 \int \frac {x}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx+12 \int \frac {x \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx+\int \frac {10+x}{9+x} \, dx+\int \frac {x^4}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-\int \frac {x^2 (10+x) \left (x^2+6 \log ((-1+x) x)\right )}{(9+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx\\ &=-\left (2 \int \frac {-1+2 x}{(-1+x) x \log ((-1+x) x)} \, dx\right )+2 \int \left (\frac {6 x^2+9 \log ((-1+x) x)+x \log ((-1+x) x)}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}+\frac {6 x^2+9 \log ((-1+x) x)+x \log ((-1+x) x)}{x \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}\right ) \, dx+4 \int \frac {x^3}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-6 \int \frac {1}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-6 \int \frac {1}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+6 \int \frac {x^2 \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-12 \int \frac {x}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx+12 \int \frac {x \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx+\int \left (1+\frac {1}{9+x}\right ) \, dx+\int \frac {x^4}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-\int \left (-\frac {9 \left (x^2+6 \log ((-1+x) x)\right )}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}+\frac {81 \left (x^2+6 \log ((-1+x) x)\right )}{(9+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )}+\frac {x^3+6 x \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}+\frac {x^4+6 x^2 \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)}\right ) \, dx\\ &=x+\log (9+x)-2 \int \frac {-1+2 x}{(-1+x) x \log ((-1+x) x)} \, dx+2 \int \frac {6 x^2+9 \log ((-1+x) x)+x \log ((-1+x) x)}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+2 \int \frac {6 x^2+9 \log ((-1+x) x)+x \log ((-1+x) x)}{x \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+4 \int \frac {x^3}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-6 \int \frac {1}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-6 \int \frac {1}{(-1+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+6 \int \frac {x^2 \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx+9 \int \frac {x^2+6 \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-12 \int \frac {x}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx+12 \int \frac {x \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-81 \int \frac {x^2+6 \log ((-1+x) x)}{(9+x) \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right )} \, dx+\int \frac {x^4}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-\int \frac {x^3+6 x \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx-\int \frac {x^4+6 x^2 \log ((-1+x) x)}{x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.09, size = 47, normalized size = 1.88 \begin {gather*} x-2 \log (\log ((-1+x) x))+\log \left (x^4+6 x^2 \log ((-1+x) x)+9 \log ^2((-1+x) x)+x \log ^2((-1+x) x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2*x^3 - 4*x^4 + (6*x - 12*x^2 - 4*x^3 + 3*x^4 + x^5)*Log[-x + x^2] + (-12*x + 6*x^2 + 6*x^3)*Log[-x
+ x^2]^2 + (-10 + 9*x + x^2)*Log[-x + x^2]^3)/((-x^4 + x^5)*Log[-x + x^2] + (-6*x^2 + 6*x^3)*Log[-x + x^2]^2
+ (-9 + 8*x + x^2)*Log[-x + x^2]^3),x]

[Out]

x - 2*Log[Log[(-1 + x)*x]] + Log[x^4 + 6*x^2*Log[(-1 + x)*x] + 9*Log[(-1 + x)*x]^2 + x*Log[(-1 + x)*x]^2]

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fricas [B]  time = 0.90, size = 55, normalized size = 2.20 \begin {gather*} x + \log \left (x + 9\right ) + \log \left (\frac {x^{4} + 6 \, x^{2} \log \left (x^{2} - x\right ) + {\left (x + 9\right )} \log \left (x^{2} - x\right )^{2}}{x + 9}\right ) - 2 \, \log \left (\log \left (x^{2} - x\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2+9*x-10)*log(x^2-x)^3+(6*x^3+6*x^2-12*x)*log(x^2-x)^2+(x^5+3*x^4-4*x^3-12*x^2+6*x)*log(x^2-x)-4
*x^4+2*x^3)/((x^2+8*x-9)*log(x^2-x)^3+(6*x^3-6*x^2)*log(x^2-x)^2+(x^5-x^4)*log(x^2-x)),x, algorithm="fricas")

[Out]

x + log(x + 9) + log((x^4 + 6*x^2*log(x^2 - x) + (x + 9)*log(x^2 - x)^2)/(x + 9)) - 2*log(log(x^2 - x))

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giac [B]  time = 0.70, size = 55, normalized size = 2.20 \begin {gather*} x + \log \left (x^{4} + 6 \, x^{2} \log \left (x^{2} - x\right ) + x \log \left (x^{2} - x\right )^{2} + 9 \, \log \left (x^{2} - x\right )^{2}\right ) - 2 \, \log \left (\log \left (x^{2} - x\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2+9*x-10)*log(x^2-x)^3+(6*x^3+6*x^2-12*x)*log(x^2-x)^2+(x^5+3*x^4-4*x^3-12*x^2+6*x)*log(x^2-x)-4
*x^4+2*x^3)/((x^2+8*x-9)*log(x^2-x)^3+(6*x^3-6*x^2)*log(x^2-x)^2+(x^5-x^4)*log(x^2-x)),x, algorithm="giac")

[Out]

x + log(x^4 + 6*x^2*log(x^2 - x) + x*log(x^2 - x)^2 + 9*log(x^2 - x)^2) - 2*log(log(x^2 - x))

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maple [B]  time = 0.07, size = 56, normalized size = 2.24

method	result	size
norman	\(x -2 \ln \left (\ln \left (x^{2}-x \right )\right )+\ln \left (x^{4}+\ln \left (x^{2}-x \right )^{2} x +6 x^{2} \ln \left (x^{2}-x \right )+9 \ln \left (x^{2}-x \right )^{2}\right )\)	\(56\)
risch	\(x +\ln \left (x +9\right )-2 \ln \left (\ln \left (x^{2}-x \right )\right )+\ln \left (\ln \left (x^{2}-x \right )^{2}+\frac {6 x^{2} \ln \left (x^{2}-x \right )}{x +9}+\frac {x^{4}}{x +9}\right )\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((x^2+9*x-10)*ln(x^2-x)^3+(6*x^3+6*x^2-12*x)*ln(x^2-x)^2+(x^5+3*x^4-4*x^3-12*x^2+6*x)*ln(x^2-x)-4*x^4+2*x^
3)/((x^2+8*x-9)*ln(x^2-x)^3+(6*x^3-6*x^2)*ln(x^2-x)^2+(x^5-x^4)*ln(x^2-x)),x,method=_RETURNVERBOSE)

[Out]

x-2*ln(ln(x^2-x))+ln(x^4+ln(x^2-x)^2*x+6*x^2*ln(x^2-x)+9*ln(x^2-x)^2)

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maxima [B]  time = 0.64, size = 70, normalized size = 2.80 \begin {gather*} x + \log \left (x + 9\right ) + \log \left (\frac {x^{4} + {\left (x + 9\right )} \log \left (x - 1\right )^{2} + 6 \, x^{2} \log \relax (x) + {\left (x + 9\right )} \log \relax (x)^{2} + 2 \, {\left (3 \, x^{2} + {\left (x + 9\right )} \log \relax (x)\right )} \log \left (x - 1\right )}{x + 9}\right ) - 2 \, \log \left (\log \left (x - 1\right ) + \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x^2+9*x-10)*log(x^2-x)^3+(6*x^3+6*x^2-12*x)*log(x^2-x)^2+(x^5+3*x^4-4*x^3-12*x^2+6*x)*log(x^2-x)-4
*x^4+2*x^3)/((x^2+8*x-9)*log(x^2-x)^3+(6*x^3-6*x^2)*log(x^2-x)^2+(x^5-x^4)*log(x^2-x)),x, algorithm="maxima")

[Out]

x + log(x + 9) + log((x^4 + (x + 9)*log(x - 1)^2 + 6*x^2*log(x) + (x + 9)*log(x)^2 + 2*(3*x^2 + (x + 9)*log(x)
)*log(x - 1))/(x + 9)) - 2*log(log(x - 1) + log(x))

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mupad [B]  time = 4.79, size = 184, normalized size = 7.36 \begin {gather*} x-3\,\ln \left (x-1\right )-\ln \left (x-\frac {1}{2}\right )-2\,\ln \left (\frac {x^3\,\ln \left (x\,\left (x-1\right )\right )\,\left (9\,x^7+126\,x^6-231\,x^5+952\,x^4-1000\,x^3+1444\,x^2-1224\,x+324\right )}{{\left (x-1\right )}^2\,{\left (x+9\right )}^4}\right )+2\,\ln \left (9\,x^7+126\,x^6-231\,x^5+952\,x^4-1000\,x^3+1444\,x^2-1224\,x+324\right )+\ln \left (\frac {\left (2\,x-1\right )\,\left (x^4+6\,x^2\,\ln \left (x\,\left (x-1\right )\right )+x\,{\ln \left (x\,\left (x-1\right )\right )}^2+9\,{\ln \left (x\,\left (x-1\right )\right )}^2\right )}{x\,\left (x^2+8\,x-9\right )}\right )-\mathrm {atan}\left (\frac {x\,735002345703105317{}\mathrm {i}-177147{}\mathrm {i}}{735002345703144683\,x+177147}\right )\,14{}\mathrm {i} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(x^2 - x)^3*(9*x + x^2 - 10) + log(x^2 - x)*(6*x - 12*x^2 - 4*x^3 + 3*x^4 + x^5) + 2*x^3 - 4*x^4 + lo
g(x^2 - x)^2*(6*x^2 - 12*x + 6*x^3))/(log(x^2 - x)^2*(6*x^2 - 6*x^3) + log(x^2 - x)*(x^4 - x^5) - log(x^2 - x)
^3*(8*x + x^2 - 9)),x)

[Out]

x - atan((x*735002345703105317i - 177147i)/(735002345703144683*x + 177147))*14i - 3*log(x - 1) - log(x - 1/2)
- 2*log((x^3*log(x*(x - 1))*(1444*x^2 - 1224*x - 1000*x^3 + 952*x^4 - 231*x^5 + 126*x^6 + 9*x^7 + 324))/((x -
1)^2*(x + 9)^4)) + 2*log(1444*x^2 - 1224*x - 1000*x^3 + 952*x^4 - 231*x^5 + 126*x^6 + 9*x^7 + 324) + log(((2*x
- 1)*(x*log(x*(x - 1))^2 + 6*x^2*log(x*(x - 1)) + 9*log(x*(x - 1))^2 + x^4))/(x*(8*x + x^2 - 9)))

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sympy [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: PolynomialError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((x**2+9*x-10)*ln(x**2-x)**3+(6*x**3+6*x**2-12*x)*ln(x**2-x)**2+(x**5+3*x**4-4*x**3-12*x**2+6*x)*ln(
x**2-x)-4*x**4+2*x**3)/((x**2+8*x-9)*ln(x**2-x)**3+(6*x**3-6*x**2)*ln(x**2-x)**2+(x**5-x**4)*ln(x**2-x)),x)

[Out]

Exception raised: PolynomialError

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