3.87.77 \(\int \frac {-2 x^2+2 e^4 x^2+2 x^3-2 x^4+e^{25} (-2 x+2 x^2)+2 x^2 \log (x)+(e^{50} (2-2 x)+2 x^2-2 x^3-2 x^5+e^{25} (4 x-2 e^4 x-6 x^2+4 x^3)+e^4 (-4 x^2+6 x^3)+(-2 e^{25} x-4 x^2+6 x^3) \log (x)) \log (e^4-x+\log (x))+(-2 x^3+6 x^4-4 x^5+e^4 (2 x^2-6 x^3+4 x^4)+e^{25} (-2 x^2+4 x^3+e^4 (2 x-4 x^2))+(2 x^2-6 x^3+4 x^4+e^{25} (2 x-4 x^2)) \log (x)) \log ^2(e^4-x+\log (x))}{e^4 x-x^2+x \log (x)} \, dx\)

Optimal. Leaf size=30 \[ \left (x-x \left (-x+\frac {e^{25}+x}{x}\right ) \log \left (e^4-x+\log (x)\right )\right )^2 \]

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Rubi [F]  time = 2.83, 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^2+2 e^4 x^2+2 x^3-2 x^4+e^{25} \left (-2 x+2 x^2\right )+2 x^2 \log (x)+\left (e^{50} (2-2 x)+2 x^2-2 x^3-2 x^5+e^{25} \left (4 x-2 e^4 x-6 x^2+4 x^3\right )+e^4 \left (-4 x^2+6 x^3\right )+\left (-2 e^{25} x-4 x^2+6 x^3\right ) \log (x)\right ) \log \left (e^4-x+\log (x)\right )+\left (-2 x^3+6 x^4-4 x^5+e^4 \left (2 x^2-6 x^3+4 x^4\right )+e^{25} \left (-2 x^2+4 x^3+e^4 \left (2 x-4 x^2\right )\right )+\left (2 x^2-6 x^3+4 x^4+e^{25} \left (2 x-4 x^2\right )\right ) \log (x)\right ) \log ^2\left (e^4-x+\log (x)\right )}{e^4 x-x^2+x \log (x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2*x^2 + 2*E^4*x^2 + 2*x^3 - 2*x^4 + E^25*(-2*x + 2*x^2) + 2*x^2*Log[x] + (E^50*(2 - 2*x) + 2*x^2 - 2*x^3
- 2*x^5 + E^25*(4*x - 2*E^4*x - 6*x^2 + 4*x^3) + E^4*(-4*x^2 + 6*x^3) + (-2*E^25*x - 4*x^2 + 6*x^3)*Log[x])*L
og[E^4 - x + Log[x]] + (-2*x^3 + 6*x^4 - 4*x^5 + E^4*(2*x^2 - 6*x^3 + 4*x^4) + E^25*(-2*x^2 + 4*x^3 + E^4*(2*x
- 4*x^2)) + (2*x^2 - 6*x^3 + 4*x^4 + E^25*(2*x - 4*x^2))*Log[x])*Log[E^4 - x + Log[x]]^2)/(E^4*x - x^2 + x*Lo
g[x]),x]

[Out]

x^2 - 2*E^25*Defer[Int][(E^4 - x + Log[x])^(-1), x] - 2*(1 - E^25)*Defer[Int][x/(E^4 - x + Log[x]), x] + 4*Def
er[Int][x^2/(E^4 - x + Log[x]), x] - 2*Defer[Int][x^3/(E^4 - x + Log[x]), x] - 2*E^50*Defer[Int][Log[E^4 - x +
Log[x]]/(x*(-E^4 + x - Log[x])), x] + 2*E^25*(2 - E^4 - E^25)*Defer[Int][Log[E^4 - x + Log[x]]/(E^4 - x + Log
[x]), x] + 2*(1 - 2*E^4 - 3*E^25)*Defer[Int][(x*Log[E^4 - x + Log[x]])/(E^4 - x + Log[x]), x] - 2*(1 - 3*E^4 -
2*E^25)*Defer[Int][(x^2*Log[E^4 - x + Log[x]])/(E^4 - x + Log[x]), x] - 2*Defer[Int][(x^4*Log[E^4 - x + Log[x
]])/(E^4 - x + Log[x]), x] - 2*E^25*Defer[Int][(Log[x]*Log[E^4 - x + Log[x]])/(E^4 - x + Log[x]), x] - 4*Defer
[Int][(x*Log[x]*Log[E^4 - x + Log[x]])/(E^4 - x + Log[x]), x] + 6*Defer[Int][(x^2*Log[x]*Log[E^4 - x + Log[x]]
)/(E^4 - x + Log[x]), x] + 2*E^25*Defer[Int][Log[E^4 - x + Log[x]]^2, x] + 2*(1 - 2*E^25)*Defer[Int][x*Log[E^4
- x + Log[x]]^2, x] - 6*Defer[Int][x^2*Log[E^4 - x + Log[x]]^2, x] + 4*Defer[Int][x^3*Log[E^4 - x + Log[x]]^2
, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (-2+2 e^4\right ) x^2+2 x^3-2 x^4+e^{25} \left (-2 x+2 x^2\right )+2 x^2 \log (x)+\left (e^{50} (2-2 x)+2 x^2-2 x^3-2 x^5+e^{25} \left (4 x-2 e^4 x-6 x^2+4 x^3\right )+e^4 \left (-4 x^2+6 x^3\right )+\left (-2 e^{25} x-4 x^2+6 x^3\right ) \log (x)\right ) \log \left (e^4-x+\log (x)\right )+\left (-2 x^3+6 x^4-4 x^5+e^4 \left (2 x^2-6 x^3+4 x^4\right )+e^{25} \left (-2 x^2+4 x^3+e^4 \left (2 x-4 x^2\right )\right )+\left (2 x^2-6 x^3+4 x^4+e^{25} \left (2 x-4 x^2\right )\right ) \log (x)\right ) \log ^2\left (e^4-x+\log (x)\right )}{e^4 x-x^2+x \log (x)} \, dx\\ &=\int \frac {2 \left (x-\left (e^{25}+x-x^2\right ) \log \left (e^4-x+\log (x)\right )\right ) \left (-e^{25}-\left (1-e^4 \left (1+e^{21}\right )\right ) x+x^2-x^3-x \left (e^4 (1-2 x)+x (-1+2 x)\right ) \log \left (e^4-x+\log (x)\right )+\log (x) \left (x+x (-1+2 x) \log \left (e^4-x+\log (x)\right )\right )\right )}{x \left (e^4-x+\log (x)\right )} \, dx\\ &=2 \int \frac {\left (x-\left (e^{25}+x-x^2\right ) \log \left (e^4-x+\log (x)\right )\right ) \left (-e^{25}-\left (1-e^4 \left (1+e^{21}\right )\right ) x+x^2-x^3-x \left (e^4 (1-2 x)+x (-1+2 x)\right ) \log \left (e^4-x+\log (x)\right )+\log (x) \left (x+x (-1+2 x) \log \left (e^4-x+\log (x)\right )\right )\right )}{x \left (e^4-x+\log (x)\right )} \, dx\\ &=2 \int \left (\frac {-e^{25}-\left (1-e^4 \left (1+e^{21}\right )\right ) x+x^2-x^3+x \log (x)}{e^4-x+\log (x)}+\frac {\left (e^{50}+2 e^{25} \left (1-\frac {1}{2} e^4 \left (1+e^{21}\right )\right ) x+\left (1-e^4 \left (2+3 e^{21}\right )\right ) x^2-\left (1-e^4 \left (3+2 e^{21}\right )\right ) x^3-x^5-e^{25} x \log (x)-2 x^2 \log (x)+3 x^3 \log (x)\right ) \log \left (e^4-x+\log (x)\right )}{x \left (e^4-x+\log (x)\right )}+(-1+2 x) \left (-e^{25}-x+x^2\right ) \log ^2\left (e^4-x+\log (x)\right )\right ) \, dx\\ &=2 \int \frac {-e^{25}-\left (1-e^4 \left (1+e^{21}\right )\right ) x+x^2-x^3+x \log (x)}{e^4-x+\log (x)} \, dx+2 \int \frac {\left (e^{50}+2 e^{25} \left (1-\frac {1}{2} e^4 \left (1+e^{21}\right )\right ) x+\left (1-e^4 \left (2+3 e^{21}\right )\right ) x^2-\left (1-e^4 \left (3+2 e^{21}\right )\right ) x^3-x^5-e^{25} x \log (x)-2 x^2 \log (x)+3 x^3 \log (x)\right ) \log \left (e^4-x+\log (x)\right )}{x \left (e^4-x+\log (x)\right )} \, dx+2 \int (-1+2 x) \left (-e^{25}-x+x^2\right ) \log ^2\left (e^4-x+\log (x)\right ) \, dx\\ &=2 \int \left (x+\frac {(-1+x) \left (-e^{25}-x+x^2\right )}{-e^4+x-\log (x)}\right ) \, dx+2 \int \left (-\frac {e^{50} \log \left (e^4-x+\log (x)\right )}{x \left (-e^4+x-\log (x)\right )}-\frac {e^{25} \left (-2+e^4+e^{25}\right ) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)}-\frac {\left (-1+2 e^4+3 e^{25}\right ) x \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)}+\frac {\left (-1+3 e^4+2 e^{25}\right ) x^2 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)}-\frac {x^4 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)}-\frac {e^{25} \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)}-\frac {2 x \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)}+\frac {3 x^2 \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)}\right ) \, dx+2 \int \left (e^{25} \log ^2\left (e^4-x+\log (x)\right )-\left (-1+2 e^{25}\right ) x \log ^2\left (e^4-x+\log (x)\right )-3 x^2 \log ^2\left (e^4-x+\log (x)\right )+2 x^3 \log ^2\left (e^4-x+\log (x)\right )\right ) \, dx\\ &=x^2+2 \int \frac {(-1+x) \left (-e^{25}-x+x^2\right )}{-e^4+x-\log (x)} \, dx-2 \int \frac {x^4 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx-4 \int \frac {x \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+4 \int x^3 \log ^2\left (e^4-x+\log (x)\right ) \, dx+6 \int \frac {x^2 \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx-6 \int x^2 \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 e^{25}\right ) \int \frac {\log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 e^{25}\right ) \int \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 e^{50}\right ) \int \frac {\log \left (e^4-x+\log (x)\right )}{x \left (-e^4+x-\log (x)\right )} \, dx+\left (2 \left (1-2 e^4-3 e^{25}\right )\right ) \int \frac {x \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 \left (1-2 e^{25}\right )\right ) \int x \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 \left (1-3 e^4-2 e^{25}\right )\right ) \int \frac {x^2 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 e^{25} \left (2-e^4-e^{25}\right )\right ) \int \frac {\log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx\\ &=x^2+2 \int \left (-\frac {e^{25}}{e^4-x+\log (x)}+\frac {\left (-1+e^{25}\right ) x}{e^4-x+\log (x)}+\frac {2 x^2}{e^4-x+\log (x)}-\frac {x^3}{e^4-x+\log (x)}\right ) \, dx-2 \int \frac {x^4 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx-4 \int \frac {x \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+4 \int x^3 \log ^2\left (e^4-x+\log (x)\right ) \, dx+6 \int \frac {x^2 \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx-6 \int x^2 \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 e^{25}\right ) \int \frac {\log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 e^{25}\right ) \int \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 e^{50}\right ) \int \frac {\log \left (e^4-x+\log (x)\right )}{x \left (-e^4+x-\log (x)\right )} \, dx+\left (2 \left (1-2 e^4-3 e^{25}\right )\right ) \int \frac {x \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 \left (1-2 e^{25}\right )\right ) \int x \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 \left (1-3 e^4-2 e^{25}\right )\right ) \int \frac {x^2 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 e^{25} \left (2-e^4-e^{25}\right )\right ) \int \frac {\log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx\\ &=x^2-2 \int \frac {x^3}{e^4-x+\log (x)} \, dx-2 \int \frac {x^4 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+4 \int \frac {x^2}{e^4-x+\log (x)} \, dx-4 \int \frac {x \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+4 \int x^3 \log ^2\left (e^4-x+\log (x)\right ) \, dx+6 \int \frac {x^2 \log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx-6 \int x^2 \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 e^{25}\right ) \int \frac {1}{e^4-x+\log (x)} \, dx-\left (2 e^{25}\right ) \int \frac {\log (x) \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 e^{25}\right ) \int \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 e^{50}\right ) \int \frac {\log \left (e^4-x+\log (x)\right )}{x \left (-e^4+x-\log (x)\right )} \, dx+\left (2 \left (1-2 e^4-3 e^{25}\right )\right ) \int \frac {x \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx+\left (2 \left (1-2 e^{25}\right )\right ) \int x \log ^2\left (e^4-x+\log (x)\right ) \, dx-\left (2 \left (1-3 e^4-2 e^{25}\right )\right ) \int \frac {x^2 \log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx-\left (2 \left (1-e^{25}\right )\right ) \int \frac {x}{e^4-x+\log (x)} \, dx+\left (2 e^{25} \left (2-e^4-e^{25}\right )\right ) \int \frac {\log \left (e^4-x+\log (x)\right )}{e^4-x+\log (x)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.10, size = 26, normalized size = 0.87 \begin {gather*} \left (x-\left (e^{25}+x-x^2\right ) \log \left (e^4-x+\log (x)\right )\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^2 + 2*E^4*x^2 + 2*x^3 - 2*x^4 + E^25*(-2*x + 2*x^2) + 2*x^2*Log[x] + (E^50*(2 - 2*x) + 2*x^2 -
2*x^3 - 2*x^5 + E^25*(4*x - 2*E^4*x - 6*x^2 + 4*x^3) + E^4*(-4*x^2 + 6*x^3) + (-2*E^25*x - 4*x^2 + 6*x^3)*Log
[x])*Log[E^4 - x + Log[x]] + (-2*x^3 + 6*x^4 - 4*x^5 + E^4*(2*x^2 - 6*x^3 + 4*x^4) + E^25*(-2*x^2 + 4*x^3 + E^
4*(2*x - 4*x^2)) + (2*x^2 - 6*x^3 + 4*x^4 + E^25*(2*x - 4*x^2))*Log[x])*Log[E^4 - x + Log[x]]^2)/(E^4*x - x^2
+ x*Log[x]),x]

[Out]

(x - (E^25 + x - x^2)*Log[E^4 - x + Log[x]])^2

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fricas [B]  time = 0.69, size = 66, normalized size = 2.20 \begin {gather*} {\left (x^{4} - 2 \, x^{3} + x^{2} - 2 \, {\left (x^{2} - x\right )} e^{25} + e^{50}\right )} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} + x^{2} + 2 \, {\left (x^{3} - x^{2} - x e^{25}\right )} \log \left (-x + e^{4} + \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^2+2*x)*exp(25)+4*x^4-6*x^3+2*x^2)*log(x)+((-4*x^2+2*x)*exp(4)+4*x^3-2*x^2)*exp(25)+(4*x^4-6
*x^3+2*x^2)*exp(4)-4*x^5+6*x^4-2*x^3)*log(log(x)+exp(4)-x)^2+((-2*x*exp(25)+6*x^3-4*x^2)*log(x)+(-2*x+2)*exp(2
5)^2+(-2*x*exp(4)+4*x^3-6*x^2+4*x)*exp(25)+(6*x^3-4*x^2)*exp(4)-2*x^5-2*x^3+2*x^2)*log(log(x)+exp(4)-x)+2*x^2*
log(x)+(2*x^2-2*x)*exp(25)+2*x^2*exp(4)-2*x^4+2*x^3-2*x^2)/(x*log(x)+x*exp(4)-x^2),x, algorithm="fricas")

[Out]

(x^4 - 2*x^3 + x^2 - 2*(x^2 - x)*e^25 + e^50)*log(-x + e^4 + log(x))^2 + x^2 + 2*(x^3 - x^2 - x*e^25)*log(-x +
e^4 + log(x))

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giac [B]  time = 0.22, size = 140, normalized size = 4.67 \begin {gather*} x^{4} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} - 2 \, x^{3} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} - 2 \, x^{2} e^{25} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} + 2 \, x^{3} \log \left (-x + e^{4} + \log \relax (x)\right ) + x^{2} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} + 2 \, x e^{25} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} - 2 \, x^{2} \log \left (-x + e^{4} + \log \relax (x)\right ) - 2 \, x e^{25} \log \left (-x + e^{4} + \log \relax (x)\right ) + e^{50} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} + x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^2+2*x)*exp(25)+4*x^4-6*x^3+2*x^2)*log(x)+((-4*x^2+2*x)*exp(4)+4*x^3-2*x^2)*exp(25)+(4*x^4-6
*x^3+2*x^2)*exp(4)-4*x^5+6*x^4-2*x^3)*log(log(x)+exp(4)-x)^2+((-2*x*exp(25)+6*x^3-4*x^2)*log(x)+(-2*x+2)*exp(2
5)^2+(-2*x*exp(4)+4*x^3-6*x^2+4*x)*exp(25)+(6*x^3-4*x^2)*exp(4)-2*x^5-2*x^3+2*x^2)*log(log(x)+exp(4)-x)+2*x^2*
log(x)+(2*x^2-2*x)*exp(25)+2*x^2*exp(4)-2*x^4+2*x^3-2*x^2)/(x*log(x)+x*exp(4)-x^2),x, algorithm="giac")

[Out]

x^4*log(-x + e^4 + log(x))^2 - 2*x^3*log(-x + e^4 + log(x))^2 - 2*x^2*e^25*log(-x + e^4 + log(x))^2 + 2*x^3*lo
g(-x + e^4 + log(x)) + x^2*log(-x + e^4 + log(x))^2 + 2*x*e^25*log(-x + e^4 + log(x))^2 - 2*x^2*log(-x + e^4 +
log(x)) - 2*x*e^25*log(-x + e^4 + log(x)) + e^50*log(-x + e^4 + log(x))^2 + x^2

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maple [B]  time = 0.09, size = 69, normalized size = 2.30

method	result	size
risch	\(\left ({\mathrm e}^{50}-2 x^{2} {\mathrm e}^{25}+2 x \,{\mathrm e}^{25}+x^{4}-2 x^{3}+x^{2}\right ) \ln \left (\ln \relax (x )+{\mathrm e}^{4}-x \right )^{2}+\left (-2 x \,{\mathrm e}^{25}+2 x^{3}-2 x^{2}\right ) \ln \left (\ln \relax (x )+{\mathrm e}^{4}-x \right )+x^{2}\)	\(69\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-4*x^2+2*x)*exp(25)+4*x^4-6*x^3+2*x^2)*ln(x)+((-4*x^2+2*x)*exp(4)+4*x^3-2*x^2)*exp(25)+(4*x^4-6*x^3+2*
x^2)*exp(4)-4*x^5+6*x^4-2*x^3)*ln(ln(x)+exp(4)-x)^2+((-2*x*exp(25)+6*x^3-4*x^2)*ln(x)+(-2*x+2)*exp(25)^2+(-2*x
*exp(4)+4*x^3-6*x^2+4*x)*exp(25)+(6*x^3-4*x^2)*exp(4)-2*x^5-2*x^3+2*x^2)*ln(ln(x)+exp(4)-x)+2*x^2*ln(x)+(2*x^2
-2*x)*exp(25)+2*x^2*exp(4)-2*x^4+2*x^3-2*x^2)/(x*ln(x)+x*exp(4)-x^2),x,method=_RETURNVERBOSE)

[Out]

(exp(50)-2*x^2*exp(25)+2*x*exp(25)+x^4-2*x^3+x^2)*ln(ln(x)+exp(4)-x)^2+(-2*x*exp(25)+2*x^3-2*x^2)*ln(ln(x)+exp
(4)-x)+x^2

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maxima [B]  time = 0.40, size = 68, normalized size = 2.27 \begin {gather*} {\left (x^{4} - 2 \, x^{3} - x^{2} {\left (2 \, e^{25} - 1\right )} + 2 \, x e^{25} + e^{50}\right )} \log \left (-x + e^{4} + \log \relax (x)\right )^{2} + x^{2} + 2 \, {\left (x^{3} - x^{2} - x e^{25}\right )} \log \left (-x + e^{4} + \log \relax (x)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x^2+2*x)*exp(25)+4*x^4-6*x^3+2*x^2)*log(x)+((-4*x^2+2*x)*exp(4)+4*x^3-2*x^2)*exp(25)+(4*x^4-6
*x^3+2*x^2)*exp(4)-4*x^5+6*x^4-2*x^3)*log(log(x)+exp(4)-x)^2+((-2*x*exp(25)+6*x^3-4*x^2)*log(x)+(-2*x+2)*exp(2
5)^2+(-2*x*exp(4)+4*x^3-6*x^2+4*x)*exp(25)+(6*x^3-4*x^2)*exp(4)-2*x^5-2*x^3+2*x^2)*log(log(x)+exp(4)-x)+2*x^2*
log(x)+(2*x^2-2*x)*exp(25)+2*x^2*exp(4)-2*x^4+2*x^3-2*x^2)/(x*log(x)+x*exp(4)-x^2),x, algorithm="maxima")

[Out]

(x^4 - 2*x^3 - x^2*(2*e^25 - 1) + 2*x*e^25 + e^50)*log(-x + e^4 + log(x))^2 + x^2 + 2*(x^3 - x^2 - x*e^25)*log
(-x + e^4 + log(x))

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mupad [B]  time = 6.58, size = 70, normalized size = 2.33 \begin {gather*} {\ln \left ({\mathrm {e}}^4-x+\ln \relax (x)\right )}^2\,\left (x^4-2\,x^3+\left (1-2\,{\mathrm {e}}^{25}\right )\,x^2+2\,{\mathrm {e}}^{25}\,x+{\mathrm {e}}^{50}\right )-\ln \left ({\mathrm {e}}^4-x+\ln \relax (x)\right )\,\left (-2\,x^3+2\,x^2+2\,{\mathrm {e}}^{25}\,x\right )+x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2*log(x) - exp(25)*(2*x - 2*x^2) + 2*x^2*exp(4) + log(exp(4) - x + log(x))^2*(log(x)*(exp(25)*(2*x -
4*x^2) + 2*x^2 - 6*x^3 + 4*x^4) + exp(25)*(exp(4)*(2*x - 4*x^2) - 2*x^2 + 4*x^3) + exp(4)*(2*x^2 - 6*x^3 + 4*x
^4) - 2*x^3 + 6*x^4 - 4*x^5) - log(exp(4) - x + log(x))*(log(x)*(2*x*exp(25) + 4*x^2 - 6*x^3) + exp(4)*(4*x^2
- 6*x^3) - exp(25)*(4*x - 2*x*exp(4) - 6*x^2 + 4*x^3) - 2*x^2 + 2*x^3 + 2*x^5 + exp(50)*(2*x - 2)) - 2*x^2 + 2
*x^3 - 2*x^4)/(x*exp(4) + x*log(x) - x^2),x)

[Out]

log(exp(4) - x + log(x))^2*(exp(50) + 2*x*exp(25) - x^2*(2*exp(25) - 1) - 2*x^3 + x^4) - log(exp(4) - x + log(
x))*(2*x*exp(25) + 2*x^2 - 2*x^3) + x^2

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sympy [B]  time = 0.77, size = 71, normalized size = 2.37 \begin {gather*} x^{2} + \left (2 x^{3} - 2 x^{2} - 2 x e^{25}\right ) \log {\left (- x + \log {\relax (x )} + e^{4} \right )} + \left (x^{4} - 2 x^{3} - 2 x^{2} e^{25} + x^{2} + 2 x e^{25} + e^{50}\right ) \log {\left (- x + \log {\relax (x )} + e^{4} \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-4*x**2+2*x)*exp(25)+4*x**4-6*x**3+2*x**2)*ln(x)+((-4*x**2+2*x)*exp(4)+4*x**3-2*x**2)*exp(25)+(4
*x**4-6*x**3+2*x**2)*exp(4)-4*x**5+6*x**4-2*x**3)*ln(ln(x)+exp(4)-x)**2+((-2*x*exp(25)+6*x**3-4*x**2)*ln(x)+(-
2*x+2)*exp(25)**2+(-2*x*exp(4)+4*x**3-6*x**2+4*x)*exp(25)+(6*x**3-4*x**2)*exp(4)-2*x**5-2*x**3+2*x**2)*ln(ln(x
)+exp(4)-x)+2*x**2*ln(x)+(2*x**2-2*x)*exp(25)+2*x**2*exp(4)-2*x**4+2*x**3-2*x**2)/(x*ln(x)+x*exp(4)-x**2),x)

[Out]

x**2 + (2*x**3 - 2*x**2 - 2*x*exp(25))*log(-x + log(x) + exp(4)) + (x**4 - 2*x**3 - 2*x**2*exp(25) + x**2 + 2*
x*exp(25) + exp(50))*log(-x + log(x) + exp(4))**2

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