3.50.26 \(\int \frac {15 x^2-5 x^3-10 x^4+(20 x^2+80 x^3) \log (x)-160 x^2 \log ^2(x)+(70 x^2-15 x^3+20 x^4+(70 x-15 x^2+20 x^3) \log (5)+(-40 x^2-160 x^3+(-40 x-160 x^2) \log (5)) \log (x)+(320 x^2+320 x \log (5)) \log ^2(x)) \log (x+\log (5))}{(x-2 x^2+x^3+(1-2 x+x^2) \log (5)+(8 x-8 x^2+(8-8 x) \log (5)) \log (x)+(16 x+16 \log (5)) \log ^2(x)) \log ^2(x+\log (5))} \, dx\)

Optimal. Leaf size=30 \[ 1+\frac {5 x \left (2 x-\frac {5 x}{1-x+4 \log (x)}\right )}{\log (x+\log (5))} \]

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Rubi [F]  time = 5.20, 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 {15 x^2-5 x^3-10 x^4+\left (20 x^2+80 x^3\right ) \log (x)-160 x^2 \log ^2(x)+\left (70 x^2-15 x^3+20 x^4+\left (70 x-15 x^2+20 x^3\right ) \log (5)+\left (-40 x^2-160 x^3+\left (-40 x-160 x^2\right ) \log (5)\right ) \log (x)+\left (320 x^2+320 x \log (5)\right ) \log ^2(x)\right ) \log (x+\log (5))}{\left (x-2 x^2+x^3+\left (1-2 x+x^2\right ) \log (5)+\left (8 x-8 x^2+(8-8 x) \log (5)\right ) \log (x)+(16 x+16 \log (5)) \log ^2(x)\right ) \log ^2(x+\log (5))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(15*x^2 - 5*x^3 - 10*x^4 + (20*x^2 + 80*x^3)*Log[x] - 160*x^2*Log[x]^2 + (70*x^2 - 15*x^3 + 20*x^4 + (70*x
- 15*x^2 + 20*x^3)*Log[5] + (-40*x^2 - 160*x^3 + (-40*x - 160*x^2)*Log[5])*Log[x] + (320*x^2 + 320*x*Log[5])*
Log[x]^2)*Log[x + Log[5]])/((x - 2*x^2 + x^3 + (1 - 2*x + x^2)*Log[5] + (8*x - 8*x^2 + (8 - 8*x)*Log[5])*Log[x
] + (16*x + 16*Log[5])*Log[x]^2)*Log[x + Log[5]]^2),x]

[Out]

15*Log[5]*Defer[Int][1/((-1 + x - 4*Log[x])*Log[x + Log[5]]^2), x] - 10*Log[5]^2*Defer[Int][1/((-1 + x - 4*Log
[x])*Log[x + Log[5]]^2), x] - 15*Defer[Int][x/((-1 + x - 4*Log[x])*Log[x + Log[5]]^2), x] + 10*Log[5]*Defer[In
t][x/((-1 + x - 4*Log[x])*Log[x + Log[5]]^2), x] - 10*Defer[Int][x^2/((-1 + x - 4*Log[x])*Log[x + Log[5]]^2),
x] - 15*Log[5]^2*Defer[Int][1/((x + Log[5])*(-1 + x - 4*Log[x])*Log[x + Log[5]]^2), x] + 10*Log[5]^3*Defer[Int
][1/((x + Log[5])*(-1 + x - 4*Log[x])*Log[x + Log[5]]^2), x] - 40*Log[5]*Defer[Int][Log[x]/((-1 + x - 4*Log[x]
)*Log[x + Log[5]]^2), x] + 40*Defer[Int][(x*Log[x])/((-1 + x - 4*Log[x])*Log[x + Log[5]]^2), x] + 40*Log[5]^2*
Defer[Int][Log[x]/((x + Log[5])*(-1 + x - 4*Log[x])*Log[x + Log[5]]^2), x] + 70*Defer[Int][x/((-1 + x - 4*Log[
x])^2*Log[x + Log[5]]), x] - 15*Defer[Int][x^2/((-1 + x - 4*Log[x])^2*Log[x + Log[5]]), x] + 20*Defer[Int][x^3
/((-1 + x - 4*Log[x])^2*Log[x + Log[5]]), x] - 40*Defer[Int][(x*Log[x])/((-1 + x - 4*Log[x])^2*Log[x + Log[5]]
), x] - 160*Defer[Int][(x^2*Log[x])/((-1 + x - 4*Log[x])^2*Log[x + Log[5]]), x] + 320*Defer[Int][(x*Log[x]^2)/
((-1 + x - 4*Log[x])^2*Log[x + Log[5]]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 x \left (-x \left (-3+x+2 x^2\right )+\left (14-3 x+4 x^2\right ) (x+\log (5)) \log (x+\log (5))-4 (1+4 x) \log (x) (-x+2 (x+\log (5)) \log (x+\log (5)))+32 \log ^2(x) (-x+2 (x+\log (5)) \log (x+\log (5)))\right )}{(x+\log (5)) (1-x+4 \log (x))^2 \log ^2(x+\log (5))} \, dx\\ &=5 \int \frac {x \left (-x \left (-3+x+2 x^2\right )+\left (14-3 x+4 x^2\right ) (x+\log (5)) \log (x+\log (5))-4 (1+4 x) \log (x) (-x+2 (x+\log (5)) \log (x+\log (5)))+32 \log ^2(x) (-x+2 (x+\log (5)) \log (x+\log (5)))\right )}{(x+\log (5)) (1-x+4 \log (x))^2 \log ^2(x+\log (5))} \, dx\\ &=5 \int \left (-\frac {x^2 (3+2 x-8 \log (x))}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))}+\frac {x \left (14-3 x+4 x^2-8 \log (x)-32 x \log (x)+64 \log ^2(x)\right )}{(-1+x-4 \log (x))^2 \log (x+\log (5))}\right ) \, dx\\ &=-\left (5 \int \frac {x^2 (3+2 x-8 \log (x))}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\right )+5 \int \frac {x \left (14-3 x+4 x^2-8 \log (x)-32 x \log (x)+64 \log ^2(x)\right )}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx\\ &=-\left (5 \int \left (\frac {x (3+2 x-8 \log (x))}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}-\frac {\log (5) (3+2 x-8 \log (x))}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}+\frac {\log ^2(5) (3+2 x-8 \log (x))}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))}\right ) \, dx\right )+5 \int \left (\frac {14 x}{(-1+x-4 \log (x))^2 \log (x+\log (5))}-\frac {3 x^2}{(-1+x-4 \log (x))^2 \log (x+\log (5))}+\frac {4 x^3}{(-1+x-4 \log (x))^2 \log (x+\log (5))}-\frac {8 x \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))}-\frac {32 x^2 \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))}+\frac {64 x \log ^2(x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))}\right ) \, dx\\ &=-\left (5 \int \frac {x (3+2 x-8 \log (x))}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\right )-15 \int \frac {x^2}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+20 \int \frac {x^3}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx-40 \int \frac {x \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+70 \int \frac {x}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx-160 \int \frac {x^2 \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+320 \int \frac {x \log ^2(x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+(5 \log (5)) \int \frac {3+2 x-8 \log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-\left (5 \log ^2(5)\right ) \int \frac {3+2 x-8 \log (x)}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\\ &=-\left (5 \int \left (\frac {3 x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}+\frac {2 x^2}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}-\frac {8 x \log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}\right ) \, dx\right )-15 \int \frac {x^2}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+20 \int \frac {x^3}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx-40 \int \frac {x \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+70 \int \frac {x}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx-160 \int \frac {x^2 \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+320 \int \frac {x \log ^2(x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+(5 \log (5)) \int \left (\frac {3}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}+\frac {2 x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}-\frac {8 \log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}\right ) \, dx-\left (5 \log ^2(5)\right ) \int \left (\frac {3}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))}+\frac {2 x}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))}-\frac {8 \log (x)}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))}\right ) \, dx\\ &=-\left (10 \int \frac {x^2}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\right )-15 \int \frac {x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-15 \int \frac {x^2}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+20 \int \frac {x^3}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+40 \int \frac {x \log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-40 \int \frac {x \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+70 \int \frac {x}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx-160 \int \frac {x^2 \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+320 \int \frac {x \log ^2(x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+(10 \log (5)) \int \frac {x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx+(15 \log (5)) \int \frac {1}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-(40 \log (5)) \int \frac {\log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-\left (10 \log ^2(5)\right ) \int \frac {x}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-\left (15 \log ^2(5)\right ) \int \frac {1}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx+\left (40 \log ^2(5)\right ) \int \frac {\log (x)}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\\ &=-\left (10 \int \frac {x^2}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\right )-15 \int \frac {x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-15 \int \frac {x^2}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+20 \int \frac {x^3}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+40 \int \frac {x \log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-40 \int \frac {x \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+70 \int \frac {x}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx-160 \int \frac {x^2 \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+320 \int \frac {x \log ^2(x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+(10 \log (5)) \int \frac {x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx+(15 \log (5)) \int \frac {1}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-(40 \log (5)) \int \frac {\log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-\left (10 \log ^2(5)\right ) \int \left (\frac {1}{(-1+x-4 \log (x)) \log ^2(x+\log (5))}-\frac {\log (5)}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))}\right ) \, dx-\left (15 \log ^2(5)\right ) \int \frac {1}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx+\left (40 \log ^2(5)\right ) \int \frac {\log (x)}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\\ &=-\left (10 \int \frac {x^2}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\right )-15 \int \frac {x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-15 \int \frac {x^2}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+20 \int \frac {x^3}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+40 \int \frac {x \log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-40 \int \frac {x \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+70 \int \frac {x}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx-160 \int \frac {x^2 \log (x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+320 \int \frac {x \log ^2(x)}{(-1+x-4 \log (x))^2 \log (x+\log (5))} \, dx+(10 \log (5)) \int \frac {x}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx+(15 \log (5)) \int \frac {1}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-(40 \log (5)) \int \frac {\log (x)}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-\left (10 \log ^2(5)\right ) \int \frac {1}{(-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx-\left (15 \log ^2(5)\right ) \int \frac {1}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx+\left (40 \log ^2(5)\right ) \int \frac {\log (x)}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx+\left (10 \log ^3(5)\right ) \int \frac {1}{(x+\log (5)) (-1+x-4 \log (x)) \log ^2(x+\log (5))} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.07, size = 30, normalized size = 1.00 \begin {gather*} \frac {5 x^2 (3+2 x-8 \log (x))}{(-1+x-4 \log (x)) \log (x+\log (5))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(15*x^2 - 5*x^3 - 10*x^4 + (20*x^2 + 80*x^3)*Log[x] - 160*x^2*Log[x]^2 + (70*x^2 - 15*x^3 + 20*x^4 +
(70*x - 15*x^2 + 20*x^3)*Log[5] + (-40*x^2 - 160*x^3 + (-40*x - 160*x^2)*Log[5])*Log[x] + (320*x^2 + 320*x*Lo
g[5])*Log[x]^2)*Log[x + Log[5]])/((x - 2*x^2 + x^3 + (1 - 2*x + x^2)*Log[5] + (8*x - 8*x^2 + (8 - 8*x)*Log[5])
*Log[x] + (16*x + 16*Log[5])*Log[x]^2)*Log[x + Log[5]]^2),x]

[Out]

(5*x^2*(3 + 2*x - 8*Log[x]))/((-1 + x - 4*Log[x])*Log[x + Log[5]])

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fricas [A]  time = 0.70, size = 36, normalized size = 1.20 \begin {gather*} \frac {5 \, {\left (2 \, x^{3} - 8 \, x^{2} \log \relax (x) + 3 \, x^{2}\right )}}{{\left (x - 4 \, \log \relax (x) - 1\right )} \log \left (x + \log \relax (5)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((320*x*log(5)+320*x^2)*log(x)^2+((-160*x^2-40*x)*log(5)-160*x^3-40*x^2)*log(x)+(20*x^3-15*x^2+70*x
)*log(5)+20*x^4-15*x^3+70*x^2)*log(log(5)+x)-160*x^2*log(x)^2+(80*x^3+20*x^2)*log(x)-10*x^4-5*x^3+15*x^2)/((16
*log(5)+16*x)*log(x)^2+((-8*x+8)*log(5)-8*x^2+8*x)*log(x)+(x^2-2*x+1)*log(5)+x^3-2*x^2+x)/log(log(5)+x)^2,x, a
lgorithm="fricas")

[Out]

5*(2*x^3 - 8*x^2*log(x) + 3*x^2)/((x - 4*log(x) - 1)*log(x + log(5)))

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giac [A]  time = 0.33, size = 46, normalized size = 1.53 \begin {gather*} \frac {5 \, {\left (2 \, x^{3} - 8 \, x^{2} \log \relax (x) + 3 \, x^{2}\right )}}{x \log \left (x + \log \relax (5)\right ) - 4 \, \log \left (x + \log \relax (5)\right ) \log \relax (x) - \log \left (x + \log \relax (5)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((320*x*log(5)+320*x^2)*log(x)^2+((-160*x^2-40*x)*log(5)-160*x^3-40*x^2)*log(x)+(20*x^3-15*x^2+70*x
)*log(5)+20*x^4-15*x^3+70*x^2)*log(log(5)+x)-160*x^2*log(x)^2+(80*x^3+20*x^2)*log(x)-10*x^4-5*x^3+15*x^2)/((16
*log(5)+16*x)*log(x)^2+((-8*x+8)*log(5)-8*x^2+8*x)*log(x)+(x^2-2*x+1)*log(5)+x^3-2*x^2+x)/log(log(5)+x)^2,x, a
lgorithm="giac")

[Out]

5*(2*x^3 - 8*x^2*log(x) + 3*x^2)/(x*log(x + log(5)) - 4*log(x + log(5))*log(x) - log(x + log(5)))

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maple [A]  time = 0.07, size = 31, normalized size = 1.03

method	result	size
risch	\(\frac {5 \left (2 x -8 \ln \relax (x )+3\right ) x^{2}}{\left (x -4 \ln \relax (x )-1\right ) \ln \left (\ln \relax (5)+x \right )}\)	\(31\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((320*x*ln(5)+320*x^2)*ln(x)^2+((-160*x^2-40*x)*ln(5)-160*x^3-40*x^2)*ln(x)+(20*x^3-15*x^2+70*x)*ln(5)+20
*x^4-15*x^3+70*x^2)*ln(ln(5)+x)-160*x^2*ln(x)^2+(80*x^3+20*x^2)*ln(x)-10*x^4-5*x^3+15*x^2)/((16*ln(5)+16*x)*ln
(x)^2+((-8*x+8)*ln(5)-8*x^2+8*x)*ln(x)+(x^2-2*x+1)*ln(5)+x^3-2*x^2+x)/ln(ln(5)+x)^2,x,method=_RETURNVERBOSE)

[Out]

5*(2*x-8*ln(x)+3)*x^2/(x-4*ln(x)-1)/ln(ln(5)+x)

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maxima [A]  time = 0.50, size = 36, normalized size = 1.20 \begin {gather*} \frac {5 \, {\left (2 \, x^{3} - 8 \, x^{2} \log \relax (x) + 3 \, x^{2}\right )}}{{\left (x - 4 \, \log \relax (x) - 1\right )} \log \left (x + \log \relax (5)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((320*x*log(5)+320*x^2)*log(x)^2+((-160*x^2-40*x)*log(5)-160*x^3-40*x^2)*log(x)+(20*x^3-15*x^2+70*x
)*log(5)+20*x^4-15*x^3+70*x^2)*log(log(5)+x)-160*x^2*log(x)^2+(80*x^3+20*x^2)*log(x)-10*x^4-5*x^3+15*x^2)/((16
*log(5)+16*x)*log(x)^2+((-8*x+8)*log(5)-8*x^2+8*x)*log(x)+(x^2-2*x+1)*log(5)+x^3-2*x^2+x)/log(log(5)+x)^2,x, a
lgorithm="maxima")

[Out]

5*(2*x^3 - 8*x^2*log(x) + 3*x^2)/((x - 4*log(x) - 1)*log(x + log(5)))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} -\int -\frac {\ln \relax (x)\,\left (80\,x^3+20\,x^2\right )+\ln \left (x+\ln \relax (5)\right )\,\left (\ln \relax (5)\,\left (20\,x^3-15\,x^2+70\,x\right )-\ln \relax (x)\,\left (\ln \relax (5)\,\left (160\,x^2+40\,x\right )+40\,x^2+160\,x^3\right )+{\ln \relax (x)}^2\,\left (320\,x^2+320\,\ln \relax (5)\,x\right )+70\,x^2-15\,x^3+20\,x^4\right )-160\,x^2\,{\ln \relax (x)}^2+15\,x^2-5\,x^3-10\,x^4}{{\ln \left (x+\ln \relax (5)\right )}^2\,\left (x+{\ln \relax (x)}^2\,\left (16\,x+16\,\ln \relax (5)\right )-\ln \relax (x)\,\left (\ln \relax (5)\,\left (8\,x-8\right )-8\,x+8\,x^2\right )-2\,x^2+x^3+\ln \relax (5)\,\left (x^2-2\,x+1\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x)*(20*x^2 + 80*x^3) + log(x + log(5))*(log(5)*(70*x - 15*x^2 + 20*x^3) - log(x)*(log(5)*(40*x + 160*
x^2) + 40*x^2 + 160*x^3) + log(x)^2*(320*x*log(5) + 320*x^2) + 70*x^2 - 15*x^3 + 20*x^4) - 160*x^2*log(x)^2 +
15*x^2 - 5*x^3 - 10*x^4)/(log(x + log(5))^2*(x + log(x)^2*(16*x + 16*log(5)) - log(x)*(log(5)*(8*x - 8) - 8*x
+ 8*x^2) - 2*x^2 + x^3 + log(5)*(x^2 - 2*x + 1))),x)

[Out]

-int(-(log(x)*(20*x^2 + 80*x^3) + log(x + log(5))*(log(5)*(70*x - 15*x^2 + 20*x^3) - log(x)*(log(5)*(40*x + 16
0*x^2) + 40*x^2 + 160*x^3) + log(x)^2*(320*x*log(5) + 320*x^2) + 70*x^2 - 15*x^3 + 20*x^4) - 160*x^2*log(x)^2
+ 15*x^2 - 5*x^3 - 10*x^4)/(log(x + log(5))^2*(x + log(x)^2*(16*x + 16*log(5)) - log(x)*(log(5)*(8*x - 8) - 8*
x + 8*x^2) - 2*x^2 + x^3 + log(5)*(x^2 - 2*x + 1))), x)

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sympy [A]  time = 0.45, size = 32, normalized size = 1.07 \begin {gather*} \frac {10 x^{3} - 40 x^{2} \log {\relax (x )} + 15 x^{2}}{\left (x - 4 \log {\relax (x )} - 1\right ) \log {\left (x + \log {\relax (5 )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((320*x*ln(5)+320*x**2)*ln(x)**2+((-160*x**2-40*x)*ln(5)-160*x**3-40*x**2)*ln(x)+(20*x**3-15*x**2+7
0*x)*ln(5)+20*x**4-15*x**3+70*x**2)*ln(ln(5)+x)-160*x**2*ln(x)**2+(80*x**3+20*x**2)*ln(x)-10*x**4-5*x**3+15*x*
*2)/((16*ln(5)+16*x)*ln(x)**2+((-8*x+8)*ln(5)-8*x**2+8*x)*ln(x)+(x**2-2*x+1)*ln(5)+x**3-2*x**2+x)/ln(ln(5)+x)*
*2,x)

[Out]

(10*x**3 - 40*x**2*log(x) + 15*x**2)/((x - 4*log(x) - 1)*log(x + log(5)))

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