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

Optimal. Leaf size=27 \[ \frac {5-e^3-e^{\left (-e^x+x+x^2\right )^x}}{x} \]

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Rubi [F]  time = 9.13, 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 {e^x \left (-5+e^3\right )+5 x+5 x^2+e^3 \left (-x-x^2\right )+e^{\left (-e^x+x+x^2\right )^x} \left (e^x-x-x^2+\left (-e^x+x+x^2\right )^x \left (x^2-e^x x^2+2 x^3+\left (-e^x x+x^2+x^3\right ) \log \left (-e^x+x+x^2\right )\right )\right )}{e^x x^2-x^3-x^4} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

5*Defer[Int][(E^x - x - x^2)^(-1), x] - E^3*Defer[Int][(E^x - x - x^2)^(-1), x] - Defer[Int][E^(-E^x + x + x^2
)^x/(E^x - x - x^2), x] - (5 - E^3)*Defer[Int][E^x/(x^2*(E^x - x - x^2)), x] + Defer[Int][E^(x + (-E^x + x + x
^2)^x)/(x^2*(E^x - x - x^2)), x] - 5*Defer[Int][1/(x*(-E^x + x + x^2)), x] + E^3*Defer[Int][1/(x*(-E^x + x + x
^2)), x] + Defer[Int][E^(-E^x + x + x^2)^x/(x*(-E^x + x + x^2)), x] - Defer[Int][E^(-E^x + x + x^2)^x*(-E^x +
x + x^2)^(-1 + x), x] - Log[-E^x + x + x^2]*Defer[Int][E^(-E^x + x + x^2)^x*(-E^x + x + x^2)^(-1 + x), x] + De
fer[Int][E^(x + (-E^x + x + x^2)^x)*(-E^x + x + x^2)^(-1 + x), x] + Log[-E^x + x + x^2]*Defer[Int][(E^(x + (-E
^x + x + x^2)^x)*(-E^x + x + x^2)^(-1 + x))/x, x] - 2*Defer[Int][E^(-E^x + x + x^2)^x*x*(-E^x + x + x^2)^(-1 +
x), x] - Log[-E^x + x + x^2]*Defer[Int][E^(-E^x + x + x^2)^x*x*(-E^x + x + x^2)^(-1 + x), x] + Defer[Int][Def
er[Int][E^(-E^x + x + x^2)^x*(-E^x + x + x^2)^(-1 + x), x], x] - Defer[Int][Defer[Int][E^(-E^x + x + x^2)^x*(-
E^x + x + x^2)^(-1 + x), x]/(E^x - x - x^2), x] + Defer[Int][(x*Defer[Int][E^(-E^x + x + x^2)^x*(-E^x + x + x^
2)^(-1 + x), x])/(-E^x + x + x^2), x] - Defer[Int][(x^2*Defer[Int][E^(-E^x + x + x^2)^x*(-E^x + x + x^2)^(-1 +
x), x])/(-E^x + x + x^2), x] - Defer[Int][Defer[Int][(E^(x + (-E^x + x + x^2)^x)*(-E^x + x + x^2)^(-1 + x))/x
, x], x] + Defer[Int][Defer[Int][(E^(x + (-E^x + x + x^2)^x)*(-E^x + x + x^2)^(-1 + x))/x, x]/(E^x - x - x^2),
x] - Defer[Int][(x*Defer[Int][(E^(x + (-E^x + x + x^2)^x)*(-E^x + x + x^2)^(-1 + x))/x, x])/(-E^x + x + x^2),
x] + Defer[Int][(x^2*Defer[Int][(E^(x + (-E^x + x + x^2)^x)*(-E^x + x + x^2)^(-1 + x))/x, x])/(-E^x + x + x^2
), x] + Defer[Int][Defer[Int][E^(-E^x + x + x^2)^x*x*(-E^x + x + x^2)^(-1 + x), x], x] - Defer[Int][Defer[Int]
[E^(-E^x + x + x^2)^x*x*(-E^x + x + x^2)^(-1 + x), x]/(E^x - x - x^2), x] + Defer[Int][(x*Defer[Int][E^(-E^x +
x + x^2)^x*x*(-E^x + x + x^2)^(-1 + x), x])/(-E^x + x + x^2), x] - Defer[Int][(x^2*Defer[Int][E^(-E^x + x + x
^2)^x*x*(-E^x + x + x^2)^(-1 + x), x])/(-E^x + x + x^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {5}{e^x-x-x^2}-\frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2}+\frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )}+\frac {e^x \left (-5+e^3\right )}{x^2 \left (e^x-x-x^2\right )}-\frac {5}{x \left (-e^x+x+x^2\right )}+\frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )}+\frac {e^3 (1+x)}{x \left (-e^x+x+x^2\right )}-\frac {e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \left (x-e^x x+2 x^2-e^x \log \left (-e^x+x+x^2\right )+x \log \left (-e^x+x+x^2\right )+x^2 \log \left (-e^x+x+x^2\right )\right )}{x}\right ) \, dx\\ &=5 \int \frac {1}{e^x-x-x^2} \, dx-5 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx+e^3 \int \frac {1+x}{x \left (-e^x+x+x^2\right )} \, dx+\left (-5+e^3\right ) \int \frac {e^x}{x^2 \left (e^x-x-x^2\right )} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )} \, dx+\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \left (x-e^x x+2 x^2-e^x \log \left (-e^x+x+x^2\right )+x \log \left (-e^x+x+x^2\right )+x^2 \log \left (-e^x+x+x^2\right )\right )}{x} \, dx\\ &=5 \int \frac {1}{e^x-x-x^2} \, dx-5 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx+e^3 \int \left (-\frac {1}{e^x-x-x^2}+\frac {1}{x \left (-e^x+x+x^2\right )}\right ) \, dx+\left (-5+e^3\right ) \int \frac {e^x}{x^2 \left (e^x-x-x^2\right )} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )} \, dx+\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \left (x \left (1-e^x+2 x\right )+\left (-e^x+x+x^2\right ) \log \left (-e^x+x+x^2\right )\right )}{x} \, dx\\ &=5 \int \frac {1}{e^x-x-x^2} \, dx-5 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx-e^3 \int \frac {1}{e^x-x-x^2} \, dx+e^3 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx+\left (-5+e^3\right ) \int \frac {e^x}{x^2 \left (e^x-x-x^2\right )} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )} \, dx+\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )} \, dx-\int \left (e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x}+2 e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x}+e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \log \left (-e^x+x+x^2\right )+e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \log \left (-e^x+x+x^2\right )-\frac {e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \left (x+\log \left (-e^x+x+x^2\right )\right )}{x}\right ) \, dx\\ &=-\left (2 \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx\right )+5 \int \frac {1}{e^x-x-x^2} \, dx-5 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx-e^3 \int \frac {1}{e^x-x-x^2} \, dx+e^3 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx+\left (-5+e^3\right ) \int \frac {e^x}{x^2 \left (e^x-x-x^2\right )} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )} \, dx+\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )} \, dx-\int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx-\int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \log \left (-e^x+x+x^2\right ) \, dx-\int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \log \left (-e^x+x+x^2\right ) \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \left (x+\log \left (-e^x+x+x^2\right )\right )}{x} \, dx\\ &=-\left (2 \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx\right )+5 \int \frac {1}{e^x-x-x^2} \, dx-5 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx-e^3 \int \frac {1}{e^x-x-x^2} \, dx+e^3 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx+\left (-5+e^3\right ) \int \frac {e^x}{x^2 \left (e^x-x-x^2\right )} \, dx-\log \left (-e^x+x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx-\log \left (-e^x+x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )} \, dx+\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )} \, dx-\int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx+\int \left (e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x}+\frac {e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \log \left (-e^x+x+x^2\right )}{x}\right ) \, dx+\int \frac {\left (-1+e^x-2 x\right ) \int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx}{e^x-x (1+x)} \, dx+\int \frac {\left (-1+e^x-2 x\right ) \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx}{e^x-x (1+x)} \, dx\\ &=-\left (2 \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx\right )+5 \int \frac {1}{e^x-x-x^2} \, dx-5 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx-e^3 \int \frac {1}{e^x-x-x^2} \, dx+e^3 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx+\left (-5+e^3\right ) \int \frac {e^x}{x^2 \left (e^x-x-x^2\right )} \, dx-\log \left (-e^x+x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx-\log \left (-e^x+x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )} \, dx+\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )} \, dx-\int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx+\int e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \log \left (-e^x+x+x^2\right )}{x} \, dx+\int \left (\int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx-\frac {\left (-1-x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx}{-e^x+x+x^2}\right ) \, dx+\int \left (\int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx-\frac {\left (-1-x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx}{-e^x+x+x^2}\right ) \, dx\\ &=-\left (2 \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx\right )+5 \int \frac {1}{e^x-x-x^2} \, dx-5 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx-e^3 \int \frac {1}{e^x-x-x^2} \, dx+e^3 \int \frac {1}{x \left (-e^x+x+x^2\right )} \, dx+\left (-5+e^3\right ) \int \frac {e^x}{x^2 \left (e^x-x-x^2\right )} \, dx-\log \left (-e^x+x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx+\log \left (-e^x+x+x^2\right ) \int \frac {e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x}}{x} \, dx-\log \left (-e^x+x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx-\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{e^x-x-x^2} \, dx+\int \frac {e^{x+\left (-e^x+x+x^2\right )^x}}{x^2 \left (e^x-x-x^2\right )} \, dx+\int \frac {e^{\left (-e^x+x+x^2\right )^x}}{x \left (-e^x+x+x^2\right )} \, dx-\int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx+\int e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx+\int \left (\int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx\right ) \, dx-\int \frac {\left (-1-x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x} \, dx}{-e^x+x+x^2} \, dx-\int \frac {\left (-1+e^x-2 x\right ) \int \frac {e^{x+\left (-e^x+x+x^2\right )^x} \left (-e^x+x+x^2\right )^{-1+x}}{x} \, dx}{e^x-x (1+x)} \, dx+\int \left (\int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx\right ) \, dx-\int \frac {\left (-1-x+x^2\right ) \int e^{\left (-e^x+x+x^2\right )^x} x \left (-e^x+x+x^2\right )^{-1+x} \, dx}{-e^x+x+x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.18, size = 24, normalized size = 0.89 \begin {gather*} -\frac {-5+e^3+e^{\left (-e^x+x+x^2\right )^x}}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

-((-5 + E^3 + E^(-E^x + x + x^2)^x)/x)

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fricas [A]  time = 0.56, size = 21, normalized size = 0.78 \begin {gather*} -\frac {e^{3} + e^{\left ({\left (x^{2} + x - e^{x}\right )}^{x}\right )} - 5}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(e^3 + e^((x^2 + x - e^x)^x) - 5)/x

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.04, size = 31, normalized size = 1.15

method	result	size
risch	\(-\frac {{\mathrm e}^{3}}{x}+\frac {5}{x}-\frac {{\mathrm e}^{\left (-{\mathrm e}^{x}+x^{2}+x \right )^{x}}}{x}\)	\(31\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-exp(x)*x+x^3+x^2)*ln(-exp(x)+x^2+x)-exp(x)*x^2+2*x^3+x^2)*exp(x*ln(-exp(x)+x^2+x))+exp(x)-x^2-x)*exp(
exp(x*ln(-exp(x)+x^2+x)))+(exp(3)-5)*exp(x)+(-x^2-x)*exp(3)+5*x^2+5*x)/(exp(x)*x^2-x^4-x^3),x,method=_RETURNVE
RBOSE)

[Out]

-exp(3)/x+5/x-1/x*exp((-exp(x)+x^2+x)^x)

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maxima [A]  time = 0.45, size = 21, normalized size = 0.78 \begin {gather*} -\frac {e^{3} + e^{\left ({\left (x^{2} + x - e^{x}\right )}^{x}\right )} - 5}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(e^3 + e^((x^2 + x - e^x)^x) - 5)/x

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mupad [B]  time = 5.62, size = 21, normalized size = 0.78 \begin {gather*} -\frac {{\mathrm {e}}^{{\left (x-{\mathrm {e}}^x+x^2\right )}^x}+{\mathrm {e}}^3-5}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-(exp((x - exp(x) + x^2)^x) + exp(3) - 5)/x

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Timed out

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