3.7.75 \(\int \frac {(4-4 x^2) \log (5)+(-1+x^2) \log ^2(5) \log (-1+x)+((-4+4 x^2+e^7 (-4-4 x+8 x^2)) \log (5)+e^7 (-x-x^2) \log ^2(5)+(1-x^2+e^7 (1+x-2 x^2)) \log ^2(5) \log (-1+x)) \log (x)+((-4-4 x+8 x^2) \log (5)+(-x-x^2) \log ^2(5)+(1+x-2 x^2) \log ^2(5) \log (-1+x)) \log (x) \log (\frac {\log (x)}{x})}{(-16 x^2-16 x^3+16 x^4+16 x^5+(8 x^2+8 x^3-8 x^4-8 x^5) \log (5) \log (-1+x)+(-x^2-x^3+x^4+x^5) \log ^2(5) \log ^2(-1+x)) \log (x)} \, dx\)

Optimal. Leaf size=32 \[ \frac {e^7+\log \left (\frac {\log (x)}{x}\right )}{\left (x+x^2\right ) \left (-\frac {4}{\log (5)}+\log (-1+x)\right )} \]

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Rubi [F]  time = 50.41, 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 {\left (4-4 x^2\right ) \log (5)+\left (-1+x^2\right ) \log ^2(5) \log (-1+x)+\left (\left (-4+4 x^2+e^7 \left (-4-4 x+8 x^2\right )\right ) \log (5)+e^7 \left (-x-x^2\right ) \log ^2(5)+\left (1-x^2+e^7 \left (1+x-2 x^2\right )\right ) \log ^2(5) \log (-1+x)\right ) \log (x)+\left (\left (-4-4 x+8 x^2\right ) \log (5)+\left (-x-x^2\right ) \log ^2(5)+\left (1+x-2 x^2\right ) \log ^2(5) \log (-1+x)\right ) \log (x) \log \left (\frac {\log (x)}{x}\right )}{\left (-16 x^2-16 x^3+16 x^4+16 x^5+\left (8 x^2+8 x^3-8 x^4-8 x^5\right ) \log (5) \log (-1+x)+\left (-x^2-x^3+x^4+x^5\right ) \log ^2(5) \log ^2(-1+x)\right ) \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((4 - 4*x^2)*Log[5] + (-1 + x^2)*Log[5]^2*Log[-1 + x] + ((-4 + 4*x^2 + E^7*(-4 - 4*x + 8*x^2))*Log[5] + E^
7*(-x - x^2)*Log[5]^2 + (1 - x^2 + E^7*(1 + x - 2*x^2))*Log[5]^2*Log[-1 + x])*Log[x] + ((-4 - 4*x + 8*x^2)*Log
[5] + (-x - x^2)*Log[5]^2 + (1 + x - 2*x^2)*Log[5]^2*Log[-1 + x])*Log[x]*Log[Log[x]/x])/((-16*x^2 - 16*x^3 + 1
6*x^4 + 16*x^5 + (8*x^2 + 8*x^3 - 8*x^4 - 8*x^5)*Log[5]*Log[-1 + x] + (-x^2 - x^3 + x^4 + x^5)*Log[5]^2*Log[-1
+ x]^2)*Log[x]),x]

[Out]

-1/2*(E^7*Log[5])/(4 - Log[5]*Log[-1 + x]) + 4*E^7*Log[5]*Defer[Int][1/(x^2*(4 - Log[5]*Log[-1 + x])^2), x] +
E^7*Log[5]^2*Defer[Int][1/(x*(4 - Log[5]*Log[-1 + x])^2), x] - 4*E^7*Log[5]*Defer[Int][1/((1 + x)^2*(4 - Log[5
]*Log[-1 + x])^2), x] - (E^7*Log[5]^2*Defer[Int][1/((1 + x)*(4 - Log[5]*Log[-1 + x])^2), x])/2 - 4*(1 + 2*E^7)
*Log[5]*Defer[Int][1/((-1 - x)*(-4 + Log[5]*Log[-1 + x])^2), x] + 4*Log[5]*Defer[Int][1/(x^2*(-4 + Log[5]*Log[
-1 + x])^2), x] - 4*(1 + E^7)*Log[5]*Defer[Int][1/(x^2*(-4 + Log[5]*Log[-1 + x])^2), x] - 4*Log[5]*Defer[Int][
1/(x*(-4 + Log[5]*Log[-1 + x])^2), x] + 8*(1 + E^7)*Log[5]*Defer[Int][1/(x*(-4 + Log[5]*Log[-1 + x])^2), x] -
4*(1 + 2*E^7)*Log[5]*Defer[Int][1/(x*(-4 + Log[5]*Log[-1 + x])^2), x] - 4*(1 + E^7)*Log[5]*Defer[Int][1/((1 +
x)^2*(-4 + Log[5]*Log[-1 + x])^2), x] + 4*(1 + 2*E^7)*Log[5]*Defer[Int][1/((1 + x)^2*(-4 + Log[5]*Log[-1 + x])
^2), x] + 4*Log[5]*Defer[Int][1/((1 + x)*(-4 + Log[5]*Log[-1 + x])^2), x] - 8*(1 + E^7)*Log[5]*Defer[Int][1/((
1 + x)*(-4 + Log[5]*Log[-1 + x])^2), x] - (1 + 2*E^7)*Log[5]*Defer[Int][1/((-1 - x)*(-4 + Log[5]*Log[-1 + x]))
, x] - (1 + E^7)*Log[5]*Defer[Int][1/(x^2*(-4 + Log[5]*Log[-1 + x])), x] + 2*(1 + E^7)*Log[5]*Defer[Int][1/(x*
(-4 + Log[5]*Log[-1 + x])), x] - (1 + 2*E^7)*Log[5]*Defer[Int][1/(x*(-4 + Log[5]*Log[-1 + x])), x] - (1 + E^7)
*Log[5]*Defer[Int][1/((1 + x)^2*(-4 + Log[5]*Log[-1 + x])), x] + (1 + 2*E^7)*Log[5]*Defer[Int][1/((1 + x)^2*(-
4 + Log[5]*Log[-1 + x])), x] - 2*(1 + E^7)*Log[5]*Defer[Int][1/((1 + x)*(-4 + Log[5]*Log[-1 + x])), x] - 4*Log
[5]*Defer[Int][1/(x^2*(-4 + Log[5]*Log[-1 + x])^2*Log[x]), x] + 4*Log[5]*Defer[Int][1/(x*(-4 + Log[5]*Log[-1 +
x])^2*Log[x]), x] - 4*Log[5]*Defer[Int][1/((1 + x)*(-4 + Log[5]*Log[-1 + x])^2*Log[x]), x] + Log[5]^2*Defer[I
nt][Log[-1 + x]/(x^2*(-4 + Log[5]*Log[-1 + x])^2*Log[x]), x] - Log[5]^2*Defer[Int][Log[-1 + x]/(x*(-4 + Log[5]
*Log[-1 + x])^2*Log[x]), x] + Log[5]^2*Defer[Int][Log[-1 + x]/((1 + x)*(-4 + Log[5]*Log[-1 + x])^2*Log[x]), x]
- Log[5]*Defer[Int][Log[Log[x]/x]/((-1 + x)*(-4 + Log[5]*Log[-1 + x])^2), x] + ((8 - Log[5])*Log[5]*Defer[Int
][Log[Log[x]/x]/((-1 + x)*(-4 + Log[5]*Log[-1 + x])^2), x])/4 - (Log[5]*(4 + Log[5])*Defer[Int][Log[Log[x]/x]/
((-1 + x)*(-4 + Log[5]*Log[-1 + x])^2), x])/4 + 4*Log[5]*Defer[Int][Log[Log[x]/x]/(x^2*(-4 + Log[5]*Log[-1 + x
])^2), x] - 4*Log[5]*Defer[Int][Log[Log[x]/x]/(x*(-4 + Log[5]*Log[-1 + x])^2), x] + Log[5]*(4 + Log[5])*Defer[
Int][Log[Log[x]/x]/(x*(-4 + Log[5]*Log[-1 + x])^2), x] + 2*Log[5]*Defer[Int][Log[Log[x]/x]/((1 + x)^2*(-4 + Lo
g[5]*Log[-1 + x])^2), x] - ((8 - Log[5])*Log[5]*Defer[Int][Log[Log[x]/x]/((1 + x)^2*(-4 + Log[5]*Log[-1 + x])^
2), x])/2 - (Log[5]*(4 + Log[5])*Defer[Int][Log[Log[x]/x]/((1 + x)^2*(-4 + Log[5]*Log[-1 + x])^2), x])/2 + 5*L
og[5]*Defer[Int][Log[Log[x]/x]/((1 + x)*(-4 + Log[5]*Log[-1 + x])^2), x] - ((8 - Log[5])*Log[5]*Defer[Int][Log
[Log[x]/x]/((1 + x)*(-4 + Log[5]*Log[-1 + x])^2), x])/4 - (3*Log[5]*(4 + Log[5])*Defer[Int][Log[Log[x]/x]/((1
+ x)*(-4 + Log[5]*Log[-1 + x])^2), x])/4 - Log[5]^2*Defer[Int][(Log[-1 + x]*Log[Log[x]/x])/(x^2*(-4 + Log[5]*L
og[-1 + x])^2), x] + Log[5]^2*Defer[Int][(Log[-1 + x]*Log[Log[x]/x])/((1 + x)^2*(-4 + Log[5]*Log[-1 + x])^2),
x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\log (5) \left (4 \left (-1+x^2\right )+\log (x) \left (4-4 x^2+e^7 \left (4+x^2 (-8+\log (5))+x (4+\log (5))\right )+\left (4+x^2 (-8+\log (5))+x (4+\log (5))\right ) \log \left (\frac {\log (x)}{x}\right )\right )+(-1+x) \log (5) \log (-1+x) \left (-1-x+\log (x) \left (1+e^7+x+2 e^7 x+(1+2 x) \log \left (\frac {\log (x)}{x}\right )\right )\right )\right )}{(1-x) x^2 (1+x)^2 (4-\log (5) \log (-1+x))^2 \log (x)} \, dx\\ &=\log (5) \int \frac {4 \left (-1+x^2\right )+\log (x) \left (4-4 x^2+e^7 \left (4+x^2 (-8+\log (5))+x (4+\log (5))\right )+\left (4+x^2 (-8+\log (5))+x (4+\log (5))\right ) \log \left (\frac {\log (x)}{x}\right )\right )+(-1+x) \log (5) \log (-1+x) \left (-1-x+\log (x) \left (1+e^7+x+2 e^7 x+(1+2 x) \log \left (\frac {\log (x)}{x}\right )\right )\right )}{(1-x) x^2 (1+x)^2 (4-\log (5) \log (-1+x))^2 \log (x)} \, dx\\ &=\log (5) \int \left (\frac {e^7 \left (4-x^2 (8-\log (5))+x (4+\log (5))\right )}{(1-x) x^2 (1+x)^2 (4-\log (5) \log (-1+x))^2}+\frac {4}{(-1+x) (1+x)^2 (-4+\log (5) \log (-1+x))^2}-\frac {4}{(-1+x) x^2 (1+x)^2 (-4+\log (5) \log (-1+x))^2}-\frac {\left (1+e^7\right ) \log (5) \log (-1+x)}{x^2 (1+x)^2 (-4+\log (5) \log (-1+x))^2}-\frac {\left (1+2 e^7\right ) \log (5) \log (-1+x)}{x (1+x)^2 (-4+\log (5) \log (-1+x))^2}-\frac {4}{x^2 (1+x) (-4+\log (5) \log (-1+x))^2 \log (x)}+\frac {\log (5) \log (-1+x)}{x^2 (1+x)^2 (-4+\log (5) \log (-1+x))^2 \log (x)}+\frac {\log (5) \log (-1+x)}{x (1+x)^2 (-4+\log (5) \log (-1+x))^2 \log (x)}+\frac {\left (4-8 x^2 \left (1-\frac {\log (5)}{8}\right )+4 x \left (1+\frac {\log (5)}{4}\right )-\log (5) \log (-1+x)-x \log (5) \log (-1+x)+2 x^2 \log (5) \log (-1+x)\right ) \log \left (\frac {\log (x)}{x}\right )}{(1-x) x^2 (1+x)^2 (4-\log (5) \log (-1+x))^2}\right ) \, dx\\ &=\log (5) \int \frac {\left (4-8 x^2 \left (1-\frac {\log (5)}{8}\right )+4 x \left (1+\frac {\log (5)}{4}\right )-\log (5) \log (-1+x)-x \log (5) \log (-1+x)+2 x^2 \log (5) \log (-1+x)\right ) \log \left (\frac {\log (x)}{x}\right )}{(1-x) x^2 (1+x)^2 (4-\log (5) \log (-1+x))^2} \, dx+(4 \log (5)) \int \frac {1}{(-1+x) (1+x)^2 (-4+\log (5) \log (-1+x))^2} \, dx-(4 \log (5)) \int \frac {1}{(-1+x) x^2 (1+x)^2 (-4+\log (5) \log (-1+x))^2} \, dx-(4 \log (5)) \int \frac {1}{x^2 (1+x) (-4+\log (5) \log (-1+x))^2 \log (x)} \, dx+\left (e^7 \log (5)\right ) \int \frac {4-x^2 (8-\log (5))+x (4+\log (5))}{(1-x) x^2 (1+x)^2 (4-\log (5) \log (-1+x))^2} \, dx+\log ^2(5) \int \frac {\log (-1+x)}{x^2 (1+x)^2 (-4+\log (5) \log (-1+x))^2 \log (x)} \, dx+\log ^2(5) \int \frac {\log (-1+x)}{x (1+x)^2 (-4+\log (5) \log (-1+x))^2 \log (x)} \, dx-\left (\left (1+e^7\right ) \log ^2(5)\right ) \int \frac {\log (-1+x)}{x^2 (1+x)^2 (-4+\log (5) \log (-1+x))^2} \, dx-\left (\left (1+2 e^7\right ) \log ^2(5)\right ) \int \frac {\log (-1+x)}{x (1+x)^2 (-4+\log (5) \log (-1+x))^2} \, dx\\ &=\log (5) \int \frac {\left (4+x^2 (-8+\log (5))+x (4+\log (5))+\left (-1-x+2 x^2\right ) \log (5) \log (-1+x)\right ) \log \left (\frac {\log (x)}{x}\right )}{(1-x) x^2 (1+x)^2 (4-\log (5) \log (-1+x))^2} \, dx-(4 \log (5)) \int \left (\frac {1}{4 (-1+x) (-4+\log (5) \log (-1+x))^2}-\frac {1}{x^2 (-4+\log (5) \log (-1+x))^2}+\frac {1}{x (-4+\log (5) \log (-1+x))^2}-\frac {1}{2 (1+x)^2 (-4+\log (5) \log (-1+x))^2}-\frac {5}{4 (1+x) (-4+\log (5) \log (-1+x))^2}\right ) \, dx+(4 \log (5)) \int \left (-\frac {1}{2 (1+x)^2 (-4+\log (5) \log (-1+x))^2}+\frac {1}{2 \left (-1+x^2\right ) (-4+\log (5) \log (-1+x))^2}\right ) \, dx-(4 \log (5)) \int \left (\frac {1}{x^2 (-4+\log (5) \log (-1+x))^2 \log (x)}-\frac {1}{x (-4+\log (5) \log (-1+x))^2 \log (x)}+\frac {1}{(1+x) (-4+\log (5) \log (-1+x))^2 \log (x)}\right ) \, dx+\left (e^7 \log (5)\right ) \int \left (\frac {4}{x^2 (4-\log (5) \log (-1+x))^2}-\frac {4}{(1+x)^2 (4-\log (5) \log (-1+x))^2}+\frac {\log (5)}{x (4-\log (5) \log (-1+x))^2}-\frac {x \log (5)}{\left (-1+x^2\right ) (4-\log (5) \log (-1+x))^2}\right ) \, dx+\log ^2(5) \int \left (\frac {\log (-1+x)}{x (-4+\log (5) \log (-1+x))^2 \log (x)}-\frac {\log (-1+x)}{(1+x)^2 (-4+\log (5) \log (-1+x))^2 \log (x)}-\frac {\log (-1+x)}{(1+x) (-4+\log (5) \log (-1+x))^2 \log (x)}\right ) \, dx+\log ^2(5) \int \left (\frac {\log (-1+x)}{x^2 (-4+\log (5) \log (-1+x))^2 \log (x)}-\frac {2 \log (-1+x)}{x (-4+\log (5) \log (-1+x))^2 \log (x)}+\frac {\log (-1+x)}{(1+x)^2 (-4+\log (5) \log (-1+x))^2 \log (x)}+\frac {2 \log (-1+x)}{(1+x) (-4+\log (5) \log (-1+x))^2 \log (x)}\right ) \, dx-\left (\left (1+e^7\right ) \log ^2(5)\right ) \int \left (\frac {4}{x^2 (1+x)^2 \log (5) (-4+\log (5) \log (-1+x))^2}+\frac {1}{x^2 (1+x)^2 \log (5) (-4+\log (5) \log (-1+x))}\right ) \, dx-\left (\left (1+2 e^7\right ) \log ^2(5)\right ) \int \left (\frac {4}{x (1+x)^2 \log (5) (-4+\log (5) \log (-1+x))^2}+\frac {1}{x (1+x)^2 \log (5) (-4+\log (5) \log (-1+x))}\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.21, size = 33, normalized size = 1.03 \begin {gather*} \frac {\log (5) \left (e^7+\log \left (\frac {\log (x)}{x}\right )\right )}{x (1+x) (-4+\log (5) \log (-1+x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((4 - 4*x^2)*Log[5] + (-1 + x^2)*Log[5]^2*Log[-1 + x] + ((-4 + 4*x^2 + E^7*(-4 - 4*x + 8*x^2))*Log[5
] + E^7*(-x - x^2)*Log[5]^2 + (1 - x^2 + E^7*(1 + x - 2*x^2))*Log[5]^2*Log[-1 + x])*Log[x] + ((-4 - 4*x + 8*x^
2)*Log[5] + (-x - x^2)*Log[5]^2 + (1 + x - 2*x^2)*Log[5]^2*Log[-1 + x])*Log[x]*Log[Log[x]/x])/((-16*x^2 - 16*x
^3 + 16*x^4 + 16*x^5 + (8*x^2 + 8*x^3 - 8*x^4 - 8*x^5)*Log[5]*Log[-1 + x] + (-x^2 - x^3 + x^4 + x^5)*Log[5]^2*
Log[-1 + x]^2)*Log[x]),x]

[Out]

(Log[5]*(E^7 + Log[Log[x]/x]))/(x*(1 + x)*(-4 + Log[5]*Log[-1 + x]))

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fricas [A]  time = 1.00, size = 40, normalized size = 1.25 \begin {gather*} \frac {e^{7} \log \relax (5) + \log \relax (5) \log \left (\frac {\log \relax (x)}{x}\right )}{{\left (x^{2} + x\right )} \log \relax (5) \log \left (x - 1\right ) - 4 \, x^{2} - 4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2+x+1)*log(5)^2*log(x-1)+(-x^2-x)*log(5)^2+(8*x^2-4*x-4)*log(5))*log(x)*log(log(x)/x)+(((-2*
x^2+x+1)*exp(7)-x^2+1)*log(5)^2*log(x-1)+(-x^2-x)*exp(7)*log(5)^2+((8*x^2-4*x-4)*exp(7)+4*x^2-4)*log(5))*log(x
)+(x^2-1)*log(5)^2*log(x-1)+(-4*x^2+4)*log(5))/((x^5+x^4-x^3-x^2)*log(5)^2*log(x-1)^2+(-8*x^5-8*x^4+8*x^3+8*x^
2)*log(5)*log(x-1)+16*x^5+16*x^4-16*x^3-16*x^2)/log(x),x, algorithm="fricas")

[Out]

(e^7*log(5) + log(5)*log(log(x)/x))/((x^2 + x)*log(5)*log(x - 1) - 4*x^2 - 4*x)

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giac [A]  time = 0.61, size = 48, normalized size = 1.50 \begin {gather*} \frac {e^{7} \log \relax (5) - \log \relax (5) \log \relax (x) + \log \relax (5) \log \left (\log \relax (x)\right )}{x^{2} \log \relax (5) \log \left (x - 1\right ) + x \log \relax (5) \log \left (x - 1\right ) - 4 \, x^{2} - 4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2+x+1)*log(5)^2*log(x-1)+(-x^2-x)*log(5)^2+(8*x^2-4*x-4)*log(5))*log(x)*log(log(x)/x)+(((-2*
x^2+x+1)*exp(7)-x^2+1)*log(5)^2*log(x-1)+(-x^2-x)*exp(7)*log(5)^2+((8*x^2-4*x-4)*exp(7)+4*x^2-4)*log(5))*log(x
)+(x^2-1)*log(5)^2*log(x-1)+(-4*x^2+4)*log(5))/((x^5+x^4-x^3-x^2)*log(5)^2*log(x-1)^2+(-8*x^5-8*x^4+8*x^3+8*x^
2)*log(5)*log(x-1)+16*x^5+16*x^4-16*x^3-16*x^2)/log(x),x, algorithm="giac")

[Out]

(e^7*log(5) - log(5)*log(x) + log(5)*log(log(x)))/(x^2*log(5)*log(x - 1) + x*log(5)*log(x - 1) - 4*x^2 - 4*x)

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maple [C]  time = 0.21, size = 143, normalized size = 4.47

method	result	size
risch	\(\frac {\ln \relax (5) \ln \left (\ln \relax (x )\right )}{\left (x +1\right ) x \left (\ln \relax (5) \ln \left (x -1\right )-4\right )}+\frac {\left (-i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x}\right )+i \pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x}\right )^{2}+i \pi \,\mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x}\right )^{2}-i \pi \mathrm {csgn}\left (\frac {i \ln \relax (x )}{x}\right )^{3}+2 \,{\mathrm e}^{7}-2 \ln \relax (x )\right ) \ln \relax (5)}{2 \left (x +1\right ) x \left (\ln \relax (5) \ln \left (x -1\right )-4\right )}\)	\(143\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-2*x^2+x+1)*ln(5)^2*ln(x-1)+(-x^2-x)*ln(5)^2+(8*x^2-4*x-4)*ln(5))*ln(x)*ln(ln(x)/x)+(((-2*x^2+x+1)*exp(
7)-x^2+1)*ln(5)^2*ln(x-1)+(-x^2-x)*exp(7)*ln(5)^2+((8*x^2-4*x-4)*exp(7)+4*x^2-4)*ln(5))*ln(x)+(x^2-1)*ln(5)^2*
ln(x-1)+(-4*x^2+4)*ln(5))/((x^5+x^4-x^3-x^2)*ln(5)^2*ln(x-1)^2+(-8*x^5-8*x^4+8*x^3+8*x^2)*ln(5)*ln(x-1)+16*x^5
+16*x^4-16*x^3-16*x^2)/ln(x),x,method=_RETURNVERBOSE)

[Out]

ln(5)/(x+1)/x/(ln(5)*ln(x-1)-4)*ln(ln(x))+1/2*(-I*Pi*csgn(I/x)*csgn(I*ln(x))*csgn(I/x*ln(x))+I*Pi*csgn(I/x)*cs
gn(I/x*ln(x))^2+I*Pi*csgn(I*ln(x))*csgn(I/x*ln(x))^2-I*Pi*csgn(I/x*ln(x))^3+2*exp(7)-2*ln(x))*ln(5)/(x+1)/x/(l
n(5)*ln(x-1)-4)

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maxima [A]  time = 0.61, size = 48, normalized size = 1.50 \begin {gather*} -\frac {e^{7} \log \relax (5) - \log \relax (5) \log \relax (x) + \log \relax (5) \log \left (\log \relax (x)\right )}{4 \, x^{2} - {\left (x^{2} \log \relax (5) + x \log \relax (5)\right )} \log \left (x - 1\right ) + 4 \, x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x^2+x+1)*log(5)^2*log(x-1)+(-x^2-x)*log(5)^2+(8*x^2-4*x-4)*log(5))*log(x)*log(log(x)/x)+(((-2*
x^2+x+1)*exp(7)-x^2+1)*log(5)^2*log(x-1)+(-x^2-x)*exp(7)*log(5)^2+((8*x^2-4*x-4)*exp(7)+4*x^2-4)*log(5))*log(x
)+(x^2-1)*log(5)^2*log(x-1)+(-4*x^2+4)*log(5))/((x^5+x^4-x^3-x^2)*log(5)^2*log(x-1)^2+(-8*x^5-8*x^4+8*x^3+8*x^
2)*log(5)*log(x-1)+16*x^5+16*x^4-16*x^3-16*x^2)/log(x),x, algorithm="maxima")

[Out]

-(e^7*log(5) - log(5)*log(x) + log(5)*log(log(x)))/(4*x^2 - (x^2*log(5) + x*log(5))*log(x - 1) + 4*x)

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mupad [B]  time = 2.02, size = 32, normalized size = 1.00 \begin {gather*} \frac {\ln \relax (5)\,\left ({\mathrm {e}}^7+\ln \left (\frac {\ln \relax (x)}{x}\right )\right )}{x\,\left (\ln \left (x-1\right )\,\ln \relax (5)-4\right )\,\left (x+1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(log(5)*(exp(7)*(4*x - 8*x^2 + 4) - 4*x^2 + 4) + exp(7)*log(5)^2*(x + x^2) - log(x - 1)*log(5)^2*(
exp(7)*(x - 2*x^2 + 1) - x^2 + 1)) + log(5)*(4*x^2 - 4) - log(x - 1)*log(5)^2*(x^2 - 1) + log(log(x)/x)*log(x)
*(log(5)*(4*x - 8*x^2 + 4) + log(5)^2*(x + x^2) - log(x - 1)*log(5)^2*(x - 2*x^2 + 1)))/(log(x)*(16*x^2 + 16*x
^3 - 16*x^4 - 16*x^5 - log(x - 1)*log(5)*(8*x^2 + 8*x^3 - 8*x^4 - 8*x^5) + log(x - 1)^2*log(5)^2*(x^2 + x^3 -
x^4 - x^5))),x)

[Out]

(log(5)*(exp(7) + log(log(x)/x)))/(x*(log(x - 1)*log(5) - 4)*(x + 1))

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sympy [B]  time = 0.95, size = 71, normalized size = 2.22 \begin {gather*} \frac {\log {\relax (5 )} \log {\left (\frac {\log {\relax (x )}}{x} \right )}}{x^{2} \log {\relax (5 )} \log {\left (x - 1 \right )} - 4 x^{2} + x \log {\relax (5 )} \log {\left (x - 1 \right )} - 4 x} + \frac {e^{7} \log {\relax (5 )}}{- 4 x^{2} - 4 x + \left (x^{2} \log {\relax (5 )} + x \log {\relax (5 )}\right ) \log {\left (x - 1 \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-2*x**2+x+1)*ln(5)**2*ln(x-1)+(-x**2-x)*ln(5)**2+(8*x**2-4*x-4)*ln(5))*ln(x)*ln(ln(x)/x)+(((-2*x*
*2+x+1)*exp(7)-x**2+1)*ln(5)**2*ln(x-1)+(-x**2-x)*exp(7)*ln(5)**2+((8*x**2-4*x-4)*exp(7)+4*x**2-4)*ln(5))*ln(x
)+(x**2-1)*ln(5)**2*ln(x-1)+(-4*x**2+4)*ln(5))/((x**5+x**4-x**3-x**2)*ln(5)**2*ln(x-1)**2+(-8*x**5-8*x**4+8*x*
*3+8*x**2)*ln(5)*ln(x-1)+16*x**5+16*x**4-16*x**3-16*x**2)/ln(x),x)

[Out]

log(5)*log(log(x)/x)/(x**2*log(5)*log(x - 1) - 4*x**2 + x*log(5)*log(x - 1) - 4*x) + exp(7)*log(5)/(-4*x**2 -
4*x + (x**2*log(5) + x*log(5))*log(x - 1))

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