3.99.56 \(\int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} (-40+540 x^2) \, dx\)

Optimal. Leaf size=15 \[ e^{20 e^{-2 x+9 x^3}} \]

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Rubi [F]  time = 0.26, 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 e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(20*E^(-2*x + 9*x^3) - 2*x + 9*x^3)*(-40 + 540*x^2),x]

[Out]

-40*Defer[Int][E^(20*E^(-2*x + 9*x^3) - 2*x + 9*x^3), x] + 540*Defer[Int][E^(20*E^(-2*x + 9*x^3) - 2*x + 9*x^3
)*x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-40 e^{20 e^{-2 x+9 x^3}-2 x+9 x^3}+540 e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} x^2\right ) \, dx\\ &=-\left (40 \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \, dx\right )+540 \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} x^2 \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.13, size = 15, normalized size = 1.00 \begin {gather*} e^{20 e^{-2 x+9 x^3}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(20*E^(-2*x + 9*x^3) - 2*x + 9*x^3)*(-40 + 540*x^2),x]

[Out]

E^(20*E^(-2*x + 9*x^3))

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fricas [A]  time = 0.67, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((540*x^2-40)*exp(20/exp(-9*x^3+2*x))/exp(-9*x^3+2*x),x, algorithm="fricas")

[Out]

e^(20*e^(9*x^3 - 2*x))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 20 \, {\left (27 \, x^{2} - 2\right )} e^{\left (9 \, x^{3} - 2 \, x + 20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((540*x^2-40)*exp(20/exp(-9*x^3+2*x))/exp(-9*x^3+2*x),x, algorithm="giac")

[Out]

integrate(20*(27*x^2 - 2)*e^(9*x^3 - 2*x + 20*e^(9*x^3 - 2*x)), x)

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maple [A]  time = 0.05, size = 14, normalized size = 0.93

method	result	size
risch	\({\mathrm e}^{20 \,{\mathrm e}^{x \left (9 x^{2}-2\right )}}\)	\(14\)
norman	\({\mathrm e}^{20 \,{\mathrm e}^{9 x^{3}-2 x}}\)	\(16\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((540*x^2-40)*exp(20/exp(-9*x^3+2*x))/exp(-9*x^3+2*x),x,method=_RETURNVERBOSE)

[Out]

exp(20*exp(x*(9*x^2-2)))

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maxima [A]  time = 0.50, size = 13, normalized size = 0.87 \begin {gather*} e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((540*x^2-40)*exp(20/exp(-9*x^3+2*x))/exp(-9*x^3+2*x),x, algorithm="maxima")

[Out]

e^(20*e^(9*x^3 - 2*x))

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mupad [B]  time = 0.10, size = 13, normalized size = 0.87 \begin {gather*} {\mathrm {e}}^{20\,{\mathrm {e}}^{9\,x^3-2\,x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(20*exp(9*x^3 - 2*x))*exp(9*x^3 - 2*x)*(540*x^2 - 40),x)

[Out]

exp(20*exp(9*x^3 - 2*x))

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sympy [A]  time = 0.30, size = 12, normalized size = 0.80 \begin {gather*} e^{20 e^{9 x^{3} - 2 x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((540*x**2-40)*exp(20/exp(-9*x**3+2*x))/exp(-9*x**3+2*x),x)

[Out]

exp(20*exp(9*x**3 - 2*x))

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