3.91.70 \(\int \frac {1}{2} e^{-2+e^{x^2}-2 x} (-17 e^{2+x}+e^{-e^{x^2}+x} (10-10 x)+34 e^{2+x+x^2} x) \, dx\)

Optimal. Leaf size=26 \[ \frac {17}{2} e^{e^{x^2}-x}+5 e^{-2-x} x \]

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Rubi [F]  time = 0.34, 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 {1}{2} e^{-2+e^{x^2}-2 x} \left (-17 e^{2+x}+e^{-e^{x^2}+x} (10-10 x)+34 e^{2+x+x^2} x\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-2 + E^x^2 - 2*x)*(-17*E^(2 + x) + E^(-E^x^2 + x)*(10 - 10*x) + 34*E^(2 + x + x^2)*x))/2,x]

[Out]

5*E^(-2 - x) - 5*E^(-2 - x)*(1 - x) - (17*Defer[Int][E^(E^x^2 - x), x])/2 + 17*Defer[Int][E^(E^x^2 - x + x^2)*
x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int e^{-2+e^{x^2}-2 x} \left (-17 e^{2+x}+e^{-e^{x^2}+x} (10-10 x)+34 e^{2+x+x^2} x\right ) \, dx\\ &=\frac {1}{2} \int \left (-17 e^{e^{x^2}-x}-10 e^{-2-x} (-1+x)+34 e^{e^{x^2}-x+x^2} x\right ) \, dx\\ &=-\left (5 \int e^{-2-x} (-1+x) \, dx\right )-\frac {17}{2} \int e^{e^{x^2}-x} \, dx+17 \int e^{e^{x^2}-x+x^2} x \, dx\\ &=-5 e^{-2-x} (1-x)-5 \int e^{-2-x} \, dx-\frac {17}{2} \int e^{e^{x^2}-x} \, dx+17 \int e^{e^{x^2}-x+x^2} x \, dx\\ &=5 e^{-2-x}-5 e^{-2-x} (1-x)-\frac {17}{2} \int e^{e^{x^2}-x} \, dx+17 \int e^{e^{x^2}-x+x^2} x \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 26, normalized size = 1.00 \begin {gather*} \frac {1}{2} e^{-2-x} \left (17 e^{2+e^{x^2}}+10 x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-2 + E^x^2 - 2*x)*(-17*E^(2 + x) + E^(-E^x^2 + x)*(10 - 10*x) + 34*E^(2 + x + x^2)*x))/2,x]

[Out]

(E^(-2 - x)*(17*E^(2 + E^x^2) + 10*x))/2

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fricas [A]  time = 0.89, size = 37, normalized size = 1.42 \begin {gather*} \frac {1}{2} \, {\left (10 \, x e^{\left (2 \, x^{2}\right )} + 17 \, e^{\left (2 \, x^{2} + e^{\left (x^{2}\right )} + 2\right )}\right )} e^{\left (-2 \, x^{2} - x - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((-10*x+10)*exp(-exp(x^2)+x)+34*x*exp(2+x)*exp(x^2)-17*exp(2+x))/exp(2+x)/exp(-exp(x^2)+x),x, al
gorithm="fricas")

[Out]

1/2*(10*x*e^(2*x^2) + 17*e^(2*x^2 + e^(x^2) + 2))*e^(-2*x^2 - x - 2)

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giac [A]  time = 0.19, size = 24, normalized size = 0.92 \begin {gather*} \frac {1}{2} \, {\left (10 \, x e^{\left (-x\right )} + 17 \, e^{\left (-x + e^{\left (x^{2}\right )} + 2\right )}\right )} e^{\left (-2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((-10*x+10)*exp(-exp(x^2)+x)+34*x*exp(2+x)*exp(x^2)-17*exp(2+x))/exp(2+x)/exp(-exp(x^2)+x),x, al
gorithm="giac")

[Out]

1/2*(10*x*e^(-x) + 17*e^(-x + e^(x^2) + 2))*e^(-2)

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maple [A]  time = 0.06, size = 22, normalized size = 0.85

method	result	size
risch	\(5 x \,{\mathrm e}^{-x -2}+\frac {17 \,{\mathrm e}^{{\mathrm e}^{x^{2}}-x}}{2}\)	\(22\)
norman	\(\left (5 \,{\mathrm e}^{-{\mathrm e}^{x^{2}}+x} x +\frac {17 \,{\mathrm e}^{2+x}}{2}\right ) {\mathrm e}^{-x -2} {\mathrm e}^{{\mathrm e}^{x^{2}}-x}\)	\(38\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2*((-10*x+10)*exp(-exp(x^2)+x)+34*x*exp(2+x)*exp(x^2)-17*exp(2+x))/exp(2+x)/exp(-exp(x^2)+x),x,method=_R
ETURNVERBOSE)

[Out]

5*x*exp(-x-2)+17/2*exp(exp(x^2)-x)

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maxima [A]  time = 0.40, size = 31, normalized size = 1.19 \begin {gather*} 5 \, {\left (x + 1\right )} e^{\left (-x - 2\right )} + \frac {17}{2} \, e^{\left (-x + e^{\left (x^{2}\right )}\right )} - 5 \, e^{\left (-x - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((-10*x+10)*exp(-exp(x^2)+x)+34*x*exp(2+x)*exp(x^2)-17*exp(2+x))/exp(2+x)/exp(-exp(x^2)+x),x, al
gorithm="maxima")

[Out]

5*(x + 1)*e^(-x - 2) + 17/2*e^(-x + e^(x^2)) - 5*e^(-x - 2)

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mupad [B]  time = 0.17, size = 21, normalized size = 0.81 \begin {gather*} \frac {{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-2}\,\left (10\,x+17\,{\mathrm {e}}^2\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}\right )}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(- x - 2)*exp(exp(x^2) - x)*((17*exp(x + 2))/2 + (exp(x - exp(x^2))*(10*x - 10))/2 - 17*x*exp(x + 2)*e
xp(x^2)),x)

[Out]

(exp(-x)*exp(-2)*(10*x + 17*exp(2)*exp(exp(x^2))))/2

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sympy [A]  time = 0.41, size = 20, normalized size = 0.77 \begin {gather*} 5 x e^{- x - 2} + \frac {17 e^{- x + e^{x^{2}}}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2*((-10*x+10)*exp(-exp(x**2)+x)+34*x*exp(2+x)*exp(x**2)-17*exp(2+x))/exp(2+x)/exp(-exp(x**2)+x),x)

[Out]

5*x*exp(-x - 2) + 17*exp(-x + exp(x**2))/2

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