3.53.87 \(\int \frac {2^{\frac {-125-25 x^2 \log (x)}{-2+x}} (x^2)^{\frac {-125-25 x^2 \log (x)}{-2+x}} (500-250 x+(100 x^2-50 x^3) \log (x)+(125 x+50 x^2-25 x^3+(100 x^2-25 x^3) \log (x)) \log (2 x^2))}{4 x-4 x^2+x^3} \, dx\)

Optimal. Leaf size=43 \[ -4+2^{\frac {25 \left (5+x^2 \log (x)\right )}{2-x}} \left (x^2\right )^{\frac {25 \left (5+x^2 \log (x)\right )}{2-x}} \]

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Rubi [F]  time = 88.20, 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 {2^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (500-250 x+\left (100 x^2-50 x^3\right ) \log (x)+\left (125 x+50 x^2-25 x^3+\left (100 x^2-25 x^3\right ) \log (x)\right ) \log \left (2 x^2\right )\right )}{4 x-4 x^2+x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(2^((-125 - 25*x^2*Log[x])/(-2 + x))*(x^2)^((-125 - 25*x^2*Log[x])/(-2 + x))*(500 - 250*x + (100*x^2 - 50*
x^3)*Log[x] + (125*x + 50*x^2 - 25*x^3 + (100*x^2 - 25*x^3)*Log[x])*Log[2*x^2]))/(4*x - 4*x^2 + x^3),x]

[Out]

-125*Defer[Int][1/(2^((25*(5 + x^2*Log[x]))/(-2 + x))*(-2 + x)*(x^2)^((25*(5 + x^2*Log[x]))/(-2 + x))), x] + 1
25*Defer[Int][1/(2^((25*(5 + x^2*Log[x]))/(-2 + x))*x*(x^2)^((25*(5 + x^2*Log[x]))/(-2 + x))), x] - 25*Defer[I
nt][(2^((-127 + x - 25*x^2*Log[x])/(-2 + x))*Log[x])/(x^2)^((25*(5 + x^2*Log[x]))/(-2 + x)), x] - 25*Defer[Int
][(2^((-129 + 2*x - 25*x^2*Log[x])/(-2 + x))*Log[x])/((-2 + x)*(x^2)^((25*(5 + x^2*Log[x]))/(-2 + x))), x] - 2
5*Defer[Int][((x^2)^((-127 + x - 25*x^2*Log[x])/(-2 + x))*Log[2*x^2])/(2^((25*(5 + x^2*Log[x]))/(-2 + x))*(2 -
x)^2), x] + 25*Defer[Int][(2^((-129 + 2*x - 25*x^2*Log[x])/(-2 + x))*Log[2*x^2])/((2 - x)^2*(x^2)^((25*(5 + x
^2*Log[x]))/(-2 + x))), x] + 125*Defer[Int][Log[2*x^2]/(2^((25*(5 + x^2*Log[x]))/(-2 + x))*(-2 + x)^2*(x^2)^((
25*(5 + x^2*Log[x]))/(-2 + x))), x] + 25*Defer[Int][(2^((-127 + x - 25*x^2*Log[x])/(-2 + x))*Log[2*x^2])/((-2
+ x)*(x^2)^((25*(5 + x^2*Log[x]))/(-2 + x))), x] - 25*Defer[Int][((x^2)^((-127 + x - 25*x^2*Log[x])/(-2 + x))*
Log[x]*Log[2*x^2])/(2^((25*(5 + x^2*Log[x]))/(-2 + x))*(2 - x)^2), x] + 25*Defer[Int][(2^((-131 + 3*x - 25*x^2
*Log[x])/(-2 + x))*Log[x]*Log[2*x^2])/((2 - x)^2*(x^2)^((25*(5 + x^2*Log[x]))/(-2 + x))), x] + 25*Defer[Int][(
2^((-129 + 2*x - 25*x^2*Log[x])/(-2 + x))*Log[x]*Log[2*x^2])/((-2 + x)*(x^2)^((25*(5 + x^2*Log[x]))/(-2 + x)))
, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (500-250 x+\left (100 x^2-50 x^3\right ) \log (x)+\left (125 x+50 x^2-25 x^3+\left (100 x^2-25 x^3\right ) \log (x)\right ) \log \left (2 x^2\right )\right )}{x \left (4-4 x+x^2\right )} \, dx\\ &=\int \frac {2^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (500-250 x+\left (100 x^2-50 x^3\right ) \log (x)+\left (125 x+50 x^2-25 x^3+\left (100 x^2-25 x^3\right ) \log (x)\right ) \log \left (2 x^2\right )\right )}{(-2+x)^2 x} \, dx\\ &=\int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (500-250 x+\left (100 x^2-50 x^3\right ) \log (x)+\left (125 x+50 x^2-25 x^3+\left (100 x^2-25 x^3\right ) \log (x)\right ) \log \left (2 x^2\right )\right )}{(2-x)^2 x} \, dx\\ &=\int \left (-\frac {25\ 2^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (5+x^2 \log (x)\right )}{(-2+x) x}-\frac {25\ 2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (-5-2 x+x^2-4 x \log (x)+x^2 \log (x)\right ) \log \left (2 x^2\right )}{(-2+x)^2}\right ) \, dx\\ &=-\left (25 \int \frac {2^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (5+x^2 \log (x)\right )}{(-2+x) x} \, dx\right )-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (-5-2 x+x^2-4 x \log (x)+x^2 \log (x)\right ) \log \left (2 x^2\right )}{(-2+x)^2} \, dx\\ &=-\left (25 \int \frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (-5-x^2 \log (x)\right )}{(2-x) x} \, dx\right )-25 \int \left (-\frac {5\ 2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2}-\frac {2^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2}+\frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2}-\frac {2^{2-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(-2+x)^2}+\frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(-2+x)^2}\right ) \, dx\\ &=-\left (25 \int \left (\frac {5\ 2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{(-2+x) x}+\frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x)}{-2+x}\right ) \, dx\right )+25 \int \frac {2^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx+25 \int \frac {2^{2-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(-2+x)^2} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{1-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(-2+x)^2} \, dx+125 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx\\ &=-\left (25 \int \frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x)}{-2+x} \, dx\right )-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(2-x)^2} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log (x) \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} x \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(2-x)^2} \, dx-125 \int \frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{(-2+x) x} \, dx+125 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx\\ &=-\left (25 \int \left (2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x)+\frac {2^{1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x)}{-2+x}\right ) \, dx\right )-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log \left (2 x^2\right )}{(2-x)^2} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log (x) \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \left (\frac {2^{1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2}+\frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{-2+x}\right ) \, dx+25 \int \left (\frac {2^{1+\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(-2+x)^2}+\frac {2^{\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{-2+x}\right ) \, dx-125 \int \left (\frac {2^{-1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{-2+x}-\frac {2^{-1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{x}\right ) \, dx+125 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx\\ &=-\left (25 \int 2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \, dx\right )-25 \int \frac {2^{1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x)}{-2+x} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx+25 \int \frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{-2+x} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log (x) \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{1+\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(-2+x)^2} \, dx+25 \int \frac {2^{\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{-2+x} \, dx-125 \int \frac {2^{-1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{-2+x} \, dx+125 \int \frac {2^{-1+\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{x} \, dx+125 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx\\ &=-\left (25 \int 2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \, dx\right )-25 \int \frac {2^{\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x)}{-2+x} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{-2+x} \, dx-25 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{\frac {-127+x-25 x^2 \log (x)}{-2+x}} \log (x) \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{\frac {-131+3 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{(2-x)^2} \, dx+25 \int \frac {2^{\frac {-129+2 x-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log (x) \log \left (2 x^2\right )}{-2+x} \, dx-125 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{-2+x} \, dx+125 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}}}{x} \, dx+125 \int \frac {2^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \left (x^2\right )^{-\frac {25 \left (5+x^2 \log (x)\right )}{-2+x}} \log \left (2 x^2\right )}{(-2+x)^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [F]  time = 1.49, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (x^2\right )^{\frac {-125-25 x^2 \log (x)}{-2+x}} \left (500-250 x+\left (100 x^2-50 x^3\right ) \log (x)+\left (125 x+50 x^2-25 x^3+\left (100 x^2-25 x^3\right ) \log (x)\right ) \log \left (2 x^2\right )\right )}{4 x-4 x^2+x^3} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(2^((-125 - 25*x^2*Log[x])/(-2 + x))*(x^2)^((-125 - 25*x^2*Log[x])/(-2 + x))*(500 - 250*x + (100*x^2
- 50*x^3)*Log[x] + (125*x + 50*x^2 - 25*x^3 + (100*x^2 - 25*x^3)*Log[x])*Log[2*x^2]))/(4*x - 4*x^2 + x^3),x]

[Out]

Integrate[(2^((-125 - 25*x^2*Log[x])/(-2 + x))*(x^2)^((-125 - 25*x^2*Log[x])/(-2 + x))*(500 - 250*x + (100*x^2
- 50*x^3)*Log[x] + (125*x + 50*x^2 - 25*x^3 + (100*x^2 - 25*x^3)*Log[x])*Log[2*x^2]))/(4*x - 4*x^2 + x^3), x]

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fricas [A]  time = 1.13, size = 33, normalized size = 0.77 \begin {gather*} e^{\left (-\frac {25 \, {\left (2 \, x^{2} \log \relax (x)^{2} + {\left (x^{2} \log \relax (2) + 10\right )} \log \relax (x) + 5 \, \log \relax (2)\right )}}{x - 2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-25*x^3+100*x^2)*log(x)-25*x^3+50*x^2+125*x)*log(2*x^2)+(-50*x^3+100*x^2)*log(x)-250*x+500)*exp((
-25*x^2*log(x)-125)*log(2*x^2)/(x-2))/(x^3-4*x^2+4*x),x, algorithm="fricas")

[Out]

e^(-25*(2*x^2*log(x)^2 + (x^2*log(2) + 10)*log(x) + 5*log(2))/(x - 2))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {25 \, {\left ({\left (x^{3} - 2 \, x^{2} + {\left (x^{3} - 4 \, x^{2}\right )} \log \relax (x) - 5 \, x\right )} \log \left (2 \, x^{2}\right ) + 2 \, {\left (x^{3} - 2 \, x^{2}\right )} \log \relax (x) + 10 \, x - 20\right )}}{{\left (x^{3} - 4 \, x^{2} + 4 \, x\right )} \left (2 \, x^{2}\right )^{\frac {25 \, {\left (x^{2} \log \relax (x) + 5\right )}}{x - 2}}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-25*x^3+100*x^2)*log(x)-25*x^3+50*x^2+125*x)*log(2*x^2)+(-50*x^3+100*x^2)*log(x)-250*x+500)*exp((
-25*x^2*log(x)-125)*log(2*x^2)/(x-2))/(x^3-4*x^2+4*x),x, algorithm="giac")

[Out]

integrate(-25*((x^3 - 2*x^2 + (x^3 - 4*x^2)*log(x) - 5*x)*log(2*x^2) + 2*(x^3 - 2*x^2)*log(x) + 10*x - 20)/((x
^3 - 4*x^2 + 4*x)*(2*x^2)^(25*(x^2*log(x) + 5)/(x - 2))), x)

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maple [C]  time = 0.23, size = 75, normalized size = 1.74

method	result	size
risch	\({\mathrm e}^{-\frac {25 \left (5+x^{2} \ln \relax (x )\right ) \left (-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+4 \ln \relax (x )+2 \ln \relax (2)\right )}{2 \left (x -2\right )}}\)	\(75\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((-25*x^3+100*x^2)*ln(x)-25*x^3+50*x^2+125*x)*ln(2*x^2)+(-50*x^3+100*x^2)*ln(x)-250*x+500)*exp((-25*x^2*l
n(x)-125)*ln(2*x^2)/(x-2))/(x^3-4*x^2+4*x),x,method=_RETURNVERBOSE)

[Out]

exp(-25/2*(5+x^2*ln(x))*(-I*Pi*csgn(I*x^2)^3+2*I*Pi*csgn(I*x)*csgn(I*x^2)^2-I*Pi*csgn(I*x)^2*csgn(I*x^2)+4*ln(
x)+2*ln(2))/(x-2))

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maxima [B]  time = 0.60, size = 68, normalized size = 1.58 \begin {gather*} e^{\left (-25 \, x \log \relax (2) \log \relax (x) - 50 \, x \log \relax (x)^{2} - 50 \, \log \relax (2) \log \relax (x) - 100 \, \log \relax (x)^{2} - \frac {100 \, \log \relax (2) \log \relax (x)}{x - 2} - \frac {200 \, \log \relax (x)^{2}}{x - 2} - \frac {125 \, \log \relax (2)}{x - 2} - \frac {250 \, \log \relax (x)}{x - 2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-25*x^3+100*x^2)*log(x)-25*x^3+50*x^2+125*x)*log(2*x^2)+(-50*x^3+100*x^2)*log(x)-250*x+500)*exp((
-25*x^2*log(x)-125)*log(2*x^2)/(x-2))/(x^3-4*x^2+4*x),x, algorithm="maxima")

[Out]

e^(-25*x*log(2)*log(x) - 50*x*log(x)^2 - 50*log(2)*log(x) - 100*log(x)^2 - 100*log(2)*log(x)/(x - 2) - 200*log
(x)^2/(x - 2) - 125*log(2)/(x - 2) - 250*log(x)/(x - 2))

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mupad [B]  time = 3.62, size = 38, normalized size = 0.88 \begin {gather*} \frac {{\left (\frac {1}{42535295865117307932921825928971026432\,x^{250}}\right )}^{\frac {1}{x-2}}}{x^{\frac {25\,\left (x^2\,\ln \left (x^2\right )+x^2\,\ln \relax (2)\right )}{x-2}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(-(log(2*x^2)*(25*x^2*log(x) + 125))/(x - 2))*(log(x)*(100*x^2 - 50*x^3) - 250*x + log(2*x^2)*(125*x +
log(x)*(100*x^2 - 25*x^3) + 50*x^2 - 25*x^3) + 500))/(4*x - 4*x^2 + x^3),x)

[Out]

(1/(42535295865117307932921825928971026432*x^250))^(1/(x - 2))/x^((25*(x^2*log(x^2) + x^2*log(2)))/(x - 2))

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sympy [A]  time = 0.84, size = 24, normalized size = 0.56 \begin {gather*} e^{\frac {\left (- 25 x^{2} \log {\relax (x )} - 125\right ) \left (2 \log {\relax (x )} + \log {\relax (2 )}\right )}{x - 2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((-25*x**3+100*x**2)*ln(x)-25*x**3+50*x**2+125*x)*ln(2*x**2)+(-50*x**3+100*x**2)*ln(x)-250*x+500)*e
xp((-25*x**2*ln(x)-125)*ln(2*x**2)/(x-2))/(x**3-4*x**2+4*x),x)

[Out]

exp((-25*x**2*log(x) - 125)*(2*log(x) + log(2))/(x - 2))

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