3.12.68 \(\int \frac {(80-480 x+e^x (-40+216 x+120 x^2)+(-16+80 x+e^x (8-32 x-40 x^2)) \log (x^2-5 x^3)) \log (\frac {-3+\log (x^2-5 x^3)}{-2 x+e^x x})+(48-240 x+e^x (-24+120 x)+(-16+e^x (8-40 x)+80 x) \log (x^2-5 x^3)) \log ^2(\frac {-3+\log (x^2-5 x^3)}{-2 x+e^x x})}{-6 x^3+30 x^4+e^x (3 x^3-15 x^4)+(2 x^3-10 x^4+e^x (-x^3+5 x^4)) \log (x^2-5 x^3)} \, dx\)

Optimal. Leaf size=35 \[ \frac {4 \log ^2\left (\frac {3-\log \left (x \left (x-5 x^2\right )\right )}{\left (2-e^x\right ) x}\right )}{x^2} \]

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Rubi [F]  time = 41.13, 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 (80-480 x+e^x \left (-40+216 x+120 x^2\right )+\left (-16+80 x+e^x \left (8-32 x-40 x^2\right )\right ) \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{-2 x+e^x x}\right )+\left (48-240 x+e^x (-24+120 x)+\left (-16+e^x (8-40 x)+80 x\right ) \log \left (x^2-5 x^3\right )\right ) \log ^2\left (\frac {-3+\log \left (x^2-5 x^3\right )}{-2 x+e^x x}\right )}{-6 x^3+30 x^4+e^x \left (3 x^3-15 x^4\right )+\left (2 x^3-10 x^4+e^x \left (-x^3+5 x^4\right )\right ) \log \left (x^2-5 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((80 - 480*x + E^x*(-40 + 216*x + 120*x^2) + (-16 + 80*x + E^x*(8 - 32*x - 40*x^2))*Log[x^2 - 5*x^3])*Log[
(-3 + Log[x^2 - 5*x^3])/(-2*x + E^x*x)] + (48 - 240*x + E^x*(-24 + 120*x) + (-16 + E^x*(8 - 40*x) + 80*x)*Log[
x^2 - 5*x^3])*Log[(-3 + Log[x^2 - 5*x^3])/(-2*x + E^x*x)]^2)/(-6*x^3 + 30*x^4 + E^x*(3*x^3 - 15*x^4) + (2*x^3
- 10*x^4 + E^x*(-x^3 + 5*x^4))*Log[x^2 - 5*x^3]),x]

[Out]

-16*Log[(3 - Log[x^2 - 5*x^3])/((2 - E^x)*x)]*Defer[Int][1/((-2 + E^x)*x^2), x] + 8*Defer[Int][(Log[(1 - 5*x)*
x^2]*Log[(-3 + Log[x^2 - 5*x^3])/((-2 + E^x)*x)])/(x^3*(3 - Log[x^2 - 5*x^3])), x] + 40*Defer[Int][(Log[(1 - 5
*x)*x^2]*Log[(-3 + Log[x^2 - 5*x^3])/((-2 + E^x)*x)])/(x^2*(3 - Log[x^2 - 5*x^3])), x] + 200*Defer[Int][(Log[(
1 - 5*x)*x^2]*Log[(-3 + Log[x^2 - 5*x^3])/((-2 + E^x)*x)])/(x*(3 - Log[x^2 - 5*x^3])), x] - 1000*Defer[Int][(L
og[(1 - 5*x)*x^2]*Log[(-3 + Log[x^2 - 5*x^3])/((-2 + E^x)*x)])/((-1 + 5*x)*(3 - Log[x^2 - 5*x^3])), x] + 40*De
fer[Int][Log[(-3 + Log[x^2 - 5*x^3])/((-2 + E^x)*x)]/(x^3*(-3 + Log[x^2 - 5*x^3])), x] - 16*Defer[Int][Log[(-3
+ Log[x^2 - 5*x^3])/((-2 + E^x)*x)]/(x^2*(-3 + Log[x^2 - 5*x^3])), x] - 200*Defer[Int][Log[(-3 + Log[x^2 - 5*
x^3])/((-2 + E^x)*x)]/(x*(-3 + Log[x^2 - 5*x^3])), x] + 1000*Defer[Int][Log[(-3 + Log[x^2 - 5*x^3])/((-2 + E^x
)*x)]/((-1 + 5*x)*(-3 + Log[x^2 - 5*x^3])), x] + 32*Defer[Int][(Log[(1 - 5*x)*x^2]*Log[(-3 + Log[x^2 - 5*x^3])
/((-2 + E^x)*x)])/(x^2*(-3 + Log[x^2 - 5*x^3])), x] + 200*Defer[Int][(Log[(1 - 5*x)*x^2]*Log[(-3 + Log[x^2 - 5
*x^3])/((-2 + E^x)*x)])/(x*(-3 + Log[x^2 - 5*x^3])), x] - 1000*Defer[Int][(Log[(1 - 5*x)*x^2]*Log[(-3 + Log[x^
2 - 5*x^3])/((-2 + E^x)*x)])/((-1 + 5*x)*(-3 + Log[x^2 - 5*x^3])), x] - 8*Defer[Int][Log[(-3 + Log[x^2 - 5*x^3
])/((-2 + E^x)*x)]^2/x^3, x] - 32*Defer[Int][Defer[Int][1/((-2 + E^x)*x^2), x]/(-2 + E^x), x] + 16*Defer[Int][
(Log[(1 - 5*x)*x^2]*Defer[Int][1/((-2 + E^x)*x^2), x])/(x*(3 - Log[x^2 - 5*x^3])), x] - 80*Defer[Int][(Log[(1
- 5*x)*x^2]*Defer[Int][1/((-2 + E^x)*x^2), x])/((-1 + 5*x)*(3 - Log[x^2 - 5*x^3])), x] + 48*Defer[Int][Defer[I
nt][1/((-2 + E^x)*x^2), x]/(-3 + Log[x^2 - 5*x^3]), x] + 80*Defer[Int][Defer[Int][1/((-2 + E^x)*x^2), x]/(x*(-
3 + Log[x^2 - 5*x^3])), x] + 80*Defer[Int][Defer[Int][1/((-2 + E^x)*x^2), x]/((-1 + 5*x)*(-3 + Log[x^2 - 5*x^3
])), x] - 16*Defer[Int][(Log[(1 - 5*x)*x^2]*Defer[Int][1/((-2 + E^x)*x^2), x])/(-3 + Log[x^2 - 5*x^3]), x] - 8
0*Defer[Int][(Log[(1 - 5*x)*x^2]*Defer[Int][1/((-2 + E^x)*x^2), x])/((-1 + 5*x)*(-3 + Log[x^2 - 5*x^3])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-\left (\left (80-480 x+e^x \left (-40+216 x+120 x^2\right )+\left (-16+80 x+e^x \left (8-32 x-40 x^2\right )\right ) \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{-2 x+e^x x}\right )\right )-\left (48-240 x+e^x (-24+120 x)+\left (-16+e^x (8-40 x)+80 x\right ) \log \left (x^2-5 x^3\right )\right ) \log ^2\left (\frac {-3+\log \left (x^2-5 x^3\right )}{-2 x+e^x x}\right )}{\left (2-e^x\right ) (1-5 x) x^3 \left (3-\log \left (x^2-5 x^3\right )\right )} \, dx\\ &=\int \left (-\frac {16 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{\left (-2+e^x\right ) x^2}-\frac {8 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right ) \left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )+3 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )-15 x \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )-\log \left (x^2-5 x^3\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )+5 x \log \left (x^2-5 x^3\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right )}{x^3 (-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )}\right ) \, dx\\ &=-\left (8 \int \frac {\log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right ) \left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )+3 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )-15 x \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )-\log \left (x^2-5 x^3\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )+5 x \log \left (x^2-5 x^3\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right )}{x^3 (-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx\right )-16 \int \frac {\log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{\left (-2+e^x\right ) x^2} \, dx\\ &=-\left (8 \int \frac {\log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right ) \left (5-27 x-15 x^2+(3-15 x) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )+(-1+5 x) \log \left (x^2-5 x^3\right ) \left (1+x+\log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right )\right )}{(1-5 x) x^3 \left (3-\log \left (x^2-5 x^3\right )\right )} \, dx\right )+16 \int \frac {\left (10-60 x+e^x \left (-5+27 x+15 x^2\right )-(-1+5 x) \left (-2+e^x (1+x)\right ) \log \left (x^2-5 x^3\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{\left (-2+e^x\right ) x (-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx-\left (16 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx\\ &=-\left (8 \int \left (\frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3 (-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )}+\frac {\log ^2\left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3}\right ) \, dx\right )+16 \int \left (-\frac {2 \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{-2+e^x}-\frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{x (-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )}\right ) \, dx-\left (16 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx\\ &=-\left (8 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3 (-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx\right )-8 \int \frac {\log ^2\left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3} \, dx-16 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{x (-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx-32 \int \frac {\int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{-2+e^x} \, dx-\left (16 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx\\ &=-\left (8 \int \frac {\log ^2\left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3} \, dx\right )-8 \int \left (-\frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3 \left (-3+\log \left (x^2-5 x^3\right )\right )}-\frac {5 \left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^2 \left (-3+\log \left (x^2-5 x^3\right )\right )}-\frac {25 \left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x \left (-3+\log \left (x^2-5 x^3\right )\right )}+\frac {125 \left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{(-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )}\right ) \, dx-16 \int \left (-\frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{x \left (-3+\log \left (x^2-5 x^3\right )\right )}+\frac {5 \left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{(-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )}\right ) \, dx-32 \int \frac {\int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{-2+e^x} \, dx-\left (16 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx\\ &=8 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3 \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx-8 \int \frac {\log ^2\left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^3} \, dx+16 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{x \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx-32 \int \frac {\int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{-2+e^x} \, dx+40 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x^2 \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx-80 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx}{(-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx+200 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{x \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx-1000 \int \frac {\left (5-27 x-15 x^2-\log \left (x^2-5 x^3\right )+4 x \log \left (x^2-5 x^3\right )+5 x^2 \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )}{(-1+5 x) \left (-3+\log \left (x^2-5 x^3\right )\right )} \, dx-\left (16 \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{\left (-2+e^x\right ) x}\right )\right ) \int \frac {1}{\left (-2+e^x\right ) x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 0.46, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (80-480 x+e^x \left (-40+216 x+120 x^2\right )+\left (-16+80 x+e^x \left (8-32 x-40 x^2\right )\right ) \log \left (x^2-5 x^3\right )\right ) \log \left (\frac {-3+\log \left (x^2-5 x^3\right )}{-2 x+e^x x}\right )+\left (48-240 x+e^x (-24+120 x)+\left (-16+e^x (8-40 x)+80 x\right ) \log \left (x^2-5 x^3\right )\right ) \log ^2\left (\frac {-3+\log \left (x^2-5 x^3\right )}{-2 x+e^x x}\right )}{-6 x^3+30 x^4+e^x \left (3 x^3-15 x^4\right )+\left (2 x^3-10 x^4+e^x \left (-x^3+5 x^4\right )\right ) \log \left (x^2-5 x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[((80 - 480*x + E^x*(-40 + 216*x + 120*x^2) + (-16 + 80*x + E^x*(8 - 32*x - 40*x^2))*Log[x^2 - 5*x^3]
)*Log[(-3 + Log[x^2 - 5*x^3])/(-2*x + E^x*x)] + (48 - 240*x + E^x*(-24 + 120*x) + (-16 + E^x*(8 - 40*x) + 80*x
)*Log[x^2 - 5*x^3])*Log[(-3 + Log[x^2 - 5*x^3])/(-2*x + E^x*x)]^2)/(-6*x^3 + 30*x^4 + E^x*(3*x^3 - 15*x^4) + (
2*x^3 - 10*x^4 + E^x*(-x^3 + 5*x^4))*Log[x^2 - 5*x^3]),x]

[Out]

Integrate[((80 - 480*x + E^x*(-40 + 216*x + 120*x^2) + (-16 + 80*x + E^x*(8 - 32*x - 40*x^2))*Log[x^2 - 5*x^3]
)*Log[(-3 + Log[x^2 - 5*x^3])/(-2*x + E^x*x)] + (48 - 240*x + E^x*(-24 + 120*x) + (-16 + E^x*(8 - 40*x) + 80*x
)*Log[x^2 - 5*x^3])*Log[(-3 + Log[x^2 - 5*x^3])/(-2*x + E^x*x)]^2)/(-6*x^3 + 30*x^4 + E^x*(3*x^3 - 15*x^4) + (
2*x^3 - 10*x^4 + E^x*(-x^3 + 5*x^4))*Log[x^2 - 5*x^3]), x]

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fricas [A]  time = 1.12, size = 31, normalized size = 0.89 \begin {gather*} \frac {4 \, \log \left (\frac {\log \left (-5 \, x^{3} + x^{2}\right ) - 3}{x e^{x} - 2 \, x}\right )^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-40*x+8)*exp(x)+80*x-16)*log(-5*x^3+x^2)+(120*x-24)*exp(x)-240*x+48)*log((log(-5*x^3+x^2)-3)/(ex
p(x)*x-2*x))^2+(((-40*x^2-32*x+8)*exp(x)+80*x-16)*log(-5*x^3+x^2)+(120*x^2+216*x-40)*exp(x)-480*x+80)*log((log
(-5*x^3+x^2)-3)/(exp(x)*x-2*x)))/(((5*x^4-x^3)*exp(x)-10*x^4+2*x^3)*log(-5*x^3+x^2)+(-15*x^4+3*x^3)*exp(x)+30*
x^4-6*x^3),x, algorithm="fricas")

[Out]

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

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {8 \, {\left ({\left (3 \, {\left (5 \, x - 1\right )} e^{x} - {\left ({\left (5 \, x - 1\right )} e^{x} - 10 \, x + 2\right )} \log \left (-5 \, x^{3} + x^{2}\right ) - 30 \, x + 6\right )} \log \left (\frac {\log \left (-5 \, x^{3} + x^{2}\right ) - 3}{x e^{x} - 2 \, x}\right )^{2} + {\left ({\left (15 \, x^{2} + 27 \, x - 5\right )} e^{x} - {\left ({\left (5 \, x^{2} + 4 \, x - 1\right )} e^{x} - 10 \, x + 2\right )} \log \left (-5 \, x^{3} + x^{2}\right ) - 60 \, x + 10\right )} \log \left (\frac {\log \left (-5 \, x^{3} + x^{2}\right ) - 3}{x e^{x} - 2 \, x}\right )\right )}}{30 \, x^{4} - 6 \, x^{3} - 3 \, {\left (5 \, x^{4} - x^{3}\right )} e^{x} - {\left (10 \, x^{4} - 2 \, x^{3} - {\left (5 \, x^{4} - x^{3}\right )} e^{x}\right )} \log \left (-5 \, x^{3} + x^{2}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-40*x+8)*exp(x)+80*x-16)*log(-5*x^3+x^2)+(120*x-24)*exp(x)-240*x+48)*log((log(-5*x^3+x^2)-3)/(ex
p(x)*x-2*x))^2+(((-40*x^2-32*x+8)*exp(x)+80*x-16)*log(-5*x^3+x^2)+(120*x^2+216*x-40)*exp(x)-480*x+80)*log((log
(-5*x^3+x^2)-3)/(exp(x)*x-2*x)))/(((5*x^4-x^3)*exp(x)-10*x^4+2*x^3)*log(-5*x^3+x^2)+(-15*x^4+3*x^3)*exp(x)+30*
x^4-6*x^3),x, algorithm="giac")

[Out]

integrate(8*((3*(5*x - 1)*e^x - ((5*x - 1)*e^x - 10*x + 2)*log(-5*x^3 + x^2) - 30*x + 6)*log((log(-5*x^3 + x^2
) - 3)/(x*e^x - 2*x))^2 + ((15*x^2 + 27*x - 5)*e^x - ((5*x^2 + 4*x - 1)*e^x - 10*x + 2)*log(-5*x^3 + x^2) - 60
*x + 10)*log((log(-5*x^3 + x^2) - 3)/(x*e^x - 2*x)))/(30*x^4 - 6*x^3 - 3*(5*x^4 - x^3)*e^x - (10*x^4 - 2*x^3 -
(5*x^4 - x^3)*e^x)*log(-5*x^3 + x^2)), x)

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maple [C]  time = 8.41, size = 47401, normalized size = 1354.31

method	result	size
risch	\(\text {Expression too large to display}\)	\(47401\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-40*x+8)*exp(x)+80*x-16)*ln(-5*x^3+x^2)+(120*x-24)*exp(x)-240*x+48)*ln((ln(-5*x^3+x^2)-3)/(exp(x)*x-2*
x))^2+(((-40*x^2-32*x+8)*exp(x)+80*x-16)*ln(-5*x^3+x^2)+(120*x^2+216*x-40)*exp(x)-480*x+80)*ln((ln(-5*x^3+x^2)
-3)/(exp(x)*x-2*x)))/(((5*x^4-x^3)*exp(x)-10*x^4+2*x^3)*ln(-5*x^3+x^2)+(-15*x^4+3*x^3)*exp(x)+30*x^4-6*x^3),x,
method=_RETURNVERBOSE)

[Out]

result too large to display

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maxima [A]  time = 0.54, size = 64, normalized size = 1.83 \begin {gather*} \frac {4 \, {\left (\log \relax (x)^{2} + 2 \, \log \relax (x) \log \left (e^{x} - 2\right ) + \log \left (e^{x} - 2\right )^{2} - 2 \, {\left (\log \relax (x) + \log \left (e^{x} - 2\right )\right )} \log \left (2 \, \log \relax (x) + \log \left (-5 \, x + 1\right ) - 3\right ) + \log \left (2 \, \log \relax (x) + \log \left (-5 \, x + 1\right ) - 3\right )^{2}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-40*x+8)*exp(x)+80*x-16)*log(-5*x^3+x^2)+(120*x-24)*exp(x)-240*x+48)*log((log(-5*x^3+x^2)-3)/(ex
p(x)*x-2*x))^2+(((-40*x^2-32*x+8)*exp(x)+80*x-16)*log(-5*x^3+x^2)+(120*x^2+216*x-40)*exp(x)-480*x+80)*log((log
(-5*x^3+x^2)-3)/(exp(x)*x-2*x)))/(((5*x^4-x^3)*exp(x)-10*x^4+2*x^3)*log(-5*x^3+x^2)+(-15*x^4+3*x^3)*exp(x)+30*
x^4-6*x^3),x, algorithm="maxima")

[Out]

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

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mupad [B]  time = 1.31, size = 33, normalized size = 0.94 \begin {gather*} \frac {4\,{\ln \left (-\frac {\ln \left (x^2-5\,x^3\right )-3}{2\,x-x\,{\mathrm {e}}^x}\right )}^2}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(-(log(x^2 - 5*x^3) - 3)/(2*x - x*exp(x)))^2*(240*x - exp(x)*(120*x - 24) + log(x^2 - 5*x^3)*(exp(x)*
(40*x - 8) - 80*x + 16) - 48) + log(-(log(x^2 - 5*x^3) - 3)/(2*x - x*exp(x)))*(480*x + log(x^2 - 5*x^3)*(exp(x
)*(32*x + 40*x^2 - 8) - 80*x + 16) - exp(x)*(216*x + 120*x^2 - 40) - 80))/(exp(x)*(3*x^3 - 15*x^4) - log(x^2 -
5*x^3)*(exp(x)*(x^3 - 5*x^4) - 2*x^3 + 10*x^4) - 6*x^3 + 30*x^4),x)

[Out]

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

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sympy [A]  time = 41.25, size = 27, normalized size = 0.77 \begin {gather*} \frac {4 \log {\left (\frac {\log {\left (- 5 x^{3} + x^{2} \right )} - 3}{x e^{x} - 2 x} \right )}^{2}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-40*x+8)*exp(x)+80*x-16)*ln(-5*x**3+x**2)+(120*x-24)*exp(x)-240*x+48)*ln((ln(-5*x**3+x**2)-3)/(e
xp(x)*x-2*x))**2+(((-40*x**2-32*x+8)*exp(x)+80*x-16)*ln(-5*x**3+x**2)+(120*x**2+216*x-40)*exp(x)-480*x+80)*ln(
(ln(-5*x**3+x**2)-3)/(exp(x)*x-2*x)))/(((5*x**4-x**3)*exp(x)-10*x**4+2*x**3)*ln(-5*x**3+x**2)+(-15*x**4+3*x**3
)*exp(x)+30*x**4-6*x**3),x)

[Out]

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

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