3.86.49 \(\int \frac {-4+e^{e^x-x+x^2} (2-e^{2+2 x}+e^x (e^2 (2-2 x)-2 x)+2 x-4 x^2)+2 \log (5)+e^x (e^2 (-3+x)+e^2 \log (5))}{4+e^{2 e^x-2 x+2 x^2}-4 x+x^2+(-4+2 x) \log (5)+\log ^2(5)+e^{e^x-x+x^2} (-4+2 x+2 \log (5))} \, dx\)

Optimal. Leaf size=28 \[ \frac {e^{2+x}+2 x}{-2+e^{e^x+(-1+x) x}+x+\log (5)} \]

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Rubi [F]  time = 20.18, 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 {-4+e^{e^x-x+x^2} \left (2-e^{2+2 x}+e^x \left (e^2 (2-2 x)-2 x\right )+2 x-4 x^2\right )+2 \log (5)+e^x \left (e^2 (-3+x)+e^2 \log (5)\right )}{4+e^{2 e^x-2 x+2 x^2}-4 x+x^2+(-4+2 x) \log (5)+\log ^2(5)+e^{e^x-x+x^2} (-4+2 x+2 \log (5))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-4 + E^(E^x - x + x^2)*(2 - E^(2 + 2*x) + E^x*(E^2*(2 - 2*x) - 2*x) + 2*x - 4*x^2) + 2*Log[5] + E^x*(E^2*
(-3 + x) + E^2*Log[5]))/(4 + E^(2*E^x - 2*x + 2*x^2) - 4*x + x^2 + (-4 + 2*x)*Log[5] + Log[5]^2 + E^(E^x - x +
x^2)*(-4 + 2*x + 2*Log[5])),x]

[Out]

Defer[Int][E^(2 + 3*x)/(-E^(E^x + x^2) - E^x*(-2 + x + Log[5])), x] + 4*Defer[Int][(E^x*x^2)/(-E^(E^x + x^2) -
E^x*(-2 + x + Log[5])), x] + (1 - Log[5])*Defer[Int][E^(2 + 3*x)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5]))^2, x
] - (2 - Log[5])*Defer[Int][E^(2 + 4*x)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5]))^2, x] + 2*(1 - Log[5])*Defer[I
nt][(E^(2*x)*x)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5]))^2, x] - 2*(2 - Log[5]*(1 + E^2*(1 - 5/Log[25])))*Defer
[Int][(E^(3*x)*x)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5]))^2, x] + Defer[Int][(E^(2 + 4*x)*x)/(E^(E^x + x^2) +
E^x*(-2 + x + Log[5]))^2, x] - 2*(5 - Log[25])*Defer[Int][(E^(2*x)*x^2)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5])
)^2, x] + 2*(1 + E^2)*Defer[Int][(E^(3*x)*x^2)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5]))^2, x] + 4*Defer[Int][(E
^(2*x)*x^3)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5]))^2, x] + 2*Defer[Int][E^x/(E^(E^x + x^2) + E^x*(-2 + x + Lo
g[5])), x] + 2*Defer[Int][E^(2 + 2*x)/(E^(E^x + x^2) + E^x*(-2 + x + Log[5])), x] + 2*Defer[Int][(E^x*x)/(E^(E
^x + x^2) + E^x*(-2 + x + Log[5])), x] - 2*(1 + E^2)*Defer[Int][(E^(2*x)*x)/(E^(E^x + x^2) + E^x*(-2 + x + Log
[5])), x]

Rubi steps

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

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Mathematica [A]  time = 0.16, size = 34, normalized size = 1.21 \begin {gather*} \frac {e^x \left (e^{2+x}+2 x\right )}{e^{e^x+x^2}+e^x (-2+x+\log (5))} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(E^x*(E^(2 + x) + 2*x))/(E^(E^x + x^2) + E^x*(-2 + x + Log[5]))

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fricas [A]  time = 0.50, size = 26, normalized size = 0.93 \begin {gather*} \frac {2 \, x + e^{\left (x + 2\right )}}{x + e^{\left (x^{2} - x + e^{x}\right )} + \log \relax (5) - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [B]  time = 0.51, size = 989, normalized size = 35.32 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(4*x^4*e^x + 8*x^3*e^x*log(5) + 4*x^2*e^x*log(5)^2 + 4*x^3*e^(x^2 + e^x) + 2*x^3*e^(2*x) + 2*x^3*e^(2*x + 2) -
18*x^3*e^x + 4*x^2*e^(x^2 + e^x)*log(5) + 4*x^2*e^(2*x)*log(5) + 4*x^2*e^(2*x + 2)*log(5) - 20*x^2*e^x*log(5)
+ 2*x*e^(2*x)*log(5)^2 + 2*x*e^(2*x + 2)*log(5)^2 - 2*x*e^x*log(5)^2 + 2*x^2*e^(x^2 + x + e^x + 2) + 2*x^2*e^
(x^2 + x + e^x) - 10*x^2*e^(x^2 + e^x) - 8*x^2*e^(2*x) + x^2*e^(3*x + 2) - 9*x^2*e^(2*x + 2) + 22*x^2*e^x + 2*
x*e^(x^2 + x + e^x + 2)*log(5) + 2*x*e^(x^2 + x + e^x)*log(5) - 2*x*e^(x^2 + e^x)*log(5) - 8*x*e^(2*x)*log(5)
+ 2*x*e^(3*x + 2)*log(5) - 10*x*e^(2*x + 2)*log(5) + 6*x*e^x*log(5) + e^(3*x + 2)*log(5)^2 - e^(2*x + 2)*log(5
)^2 + x*e^(x^2 + 2*x + e^x + 2) - 5*x*e^(x^2 + x + e^x + 2) - 4*x*e^(x^2 + x + e^x) + 2*x*e^(x^2 + e^x) + 8*x*
e^(2*x) - 4*x*e^(3*x + 2) + 11*x*e^(2*x + 2) - 4*x*e^x + e^(x^2 + 2*x + e^x + 2)*log(5) - e^(x^2 + x + e^x + 2
)*log(5) - 4*e^(3*x + 2)*log(5) + 3*e^(2*x + 2)*log(5) - 2*e^(x^2 + 2*x + e^x + 2) + e^(x^2 + x + e^x + 2) + 4
*e^(3*x + 2) - 2*e^(2*x + 2))/(2*x^4*e^x + 6*x^3*e^x*log(5) + 6*x^2*e^x*log(5)^2 + 2*x*e^x*log(5)^3 + 4*x^3*e^
(x^2 + e^x) + x^3*e^(2*x) - 13*x^3*e^x + 8*x^2*e^(x^2 + e^x)*log(5) + 3*x^2*e^(2*x)*log(5) - 27*x^2*e^x*log(5)
+ 4*x*e^(x^2 + e^x)*log(5)^2 + 3*x*e^(2*x)*log(5)^2 - 15*x*e^x*log(5)^2 + e^(2*x)*log(5)^3 - e^x*log(5)^3 + 2
*x^2*e^(2*x^2 - x + 2*e^x) + 2*x^2*e^(x^2 + x + e^x) - 18*x^2*e^(x^2 + e^x) - 6*x^2*e^(2*x) + 29*x^2*e^x + 2*x
*e^(2*x^2 - x + 2*e^x)*log(5) + 4*x*e^(x^2 + x + e^x)*log(5) - 20*x*e^(x^2 + e^x)*log(5) - 12*x*e^(2*x)*log(5)
+ 34*x*e^x*log(5) + 2*e^(x^2 + x + e^x)*log(5)^2 - 2*e^(x^2 + e^x)*log(5)^2 - 6*e^(2*x)*log(5)^2 + 5*e^x*log(
5)^2 - 5*x*e^(2*x^2 - x + 2*e^x) + x*e^(2*x^2 + 2*e^x) - 8*x*e^(x^2 + x + e^x) + 22*x*e^(x^2 + e^x) + 12*x*e^(
2*x) - 24*x*e^x - e^(2*x^2 - x + 2*e^x)*log(5) + e^(2*x^2 + 2*e^x)*log(5) - 8*e^(x^2 + x + e^x)*log(5) + 6*e^(
x^2 + e^x)*log(5) + 12*e^(2*x)*log(5) - 8*e^x*log(5) + e^(2*x^2 - x + 2*e^x) - 2*e^(2*x^2 + 2*e^x) + 8*e^(x^2
+ x + e^x) - 4*e^(x^2 + e^x) - 8*e^(2*x) + 4*e^x)

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maple [A]  time = 0.31, size = 27, normalized size = 0.96

method	result	size
risch	\(\frac {{\mathrm e}^{2+x}+2 x}{x -2+\ln \relax (5)+{\mathrm e}^{x^{2}+{\mathrm e}^{x}-x}}\)	\(27\)
norman	\(\frac {-2 \,{\mathrm e}^{x^{2}+{\mathrm e}^{x}-x}+{\mathrm e}^{2} {\mathrm e}^{x}-2 \ln \relax (5)+4}{x -2+\ln \relax (5)+{\mathrm e}^{x^{2}+{\mathrm e}^{x}-x}}\)	\(42\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-exp(2)*exp(x)^2+((-2*x+2)*exp(2)-2*x)*exp(x)-4*x^2+2*x+2)*exp(x^2+exp(x)-x)+(exp(2)*ln(5)+(x-3)*exp(2))
*exp(x)+2*ln(5)-4)/(exp(x^2+exp(x)-x)^2+(2*ln(5)+2*x-4)*exp(x^2+exp(x)-x)+ln(5)^2+(2*x-4)*ln(5)+x^2-4*x+4),x,m
ethod=_RETURNVERBOSE)

[Out]

(exp(2+x)+2*x)/(x-2+ln(5)+exp(x^2+exp(x)-x))

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maxima [A]  time = 0.65, size = 31, normalized size = 1.11 \begin {gather*} \frac {2 \, x e^{x} + e^{\left (2 \, x + 2\right )}}{{\left (x + \log \relax (5) - 2\right )} e^{x} + e^{\left (x^{2} + e^{x}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {2\,\ln \relax (5)-{\mathrm {e}}^{{\mathrm {e}}^x-x+x^2}\,\left ({\mathrm {e}}^{2\,x+2}-2\,x+{\mathrm {e}}^x\,\left (2\,x+{\mathrm {e}}^2\,\left (2\,x-2\right )\right )+4\,x^2-2\right )+{\mathrm {e}}^x\,\left ({\mathrm {e}}^2\,\ln \relax (5)+{\mathrm {e}}^2\,\left (x-3\right )\right )-4}{{\mathrm {e}}^{2\,{\mathrm {e}}^x-2\,x+2\,x^2}-4\,x+\ln \relax (5)\,\left (2\,x-4\right )+{\mathrm {e}}^{{\mathrm {e}}^x-x+x^2}\,\left (2\,x+2\,\ln \relax (5)-4\right )+{\ln \relax (5)}^2+x^2+4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.26, size = 26, normalized size = 0.93 \begin {gather*} \frac {2 x + e^{2} e^{x}}{x + e^{x^{2} - x + e^{x}} - 2 + \log {\relax (5 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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