\(\int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} (-40+540 x^2) \, dx\) [9856]

Optimal result

Integrand size = 32, antiderivative size = 15 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{20 e^{-2 x+9 x^3}} \]

[Out]

exp(20/exp(-9*x^3+2*x))

Rubi [F]

\[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=\int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx \]

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.11 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{20 e^{-2 x+9 x^3}} \]

[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))

Maple [A] (verified)

Time = 0.14 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93

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

[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)))

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \]

[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))

Sympy [A] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{20 e^{9 x^{3} - 2 x}} \]

[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))

Maxima [A] (verification not implemented)

none

Time = 0.33 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=e^{\left (20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \]

[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))

Giac [F]

\[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx=\int { 20 \, {\left (27 \, x^{2} - 2\right )} e^{\left (9 \, x^{3} - 2 \, x + 20 \, e^{\left (9 \, x^{3} - 2 \, x\right )}\right )} \,d x } \]

[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)

Mupad [B] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{20 e^{-2 x+9 x^3}-2 x+9 x^3} \left (-40+540 x^2\right ) \, dx={\mathrm {e}}^{20\,{\mathrm {e}}^{9\,x^3-2\,x}} \]

[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))