3.1.32 \(\int e^{10 x^2+x^3-e^{x^2} x^4} (20 x+3 x^2+e^{x^2} (-4 x^3-2 x^5)) \, dx\)

Optimal. Leaf size=19 \[ e^{x^2 \left (10+x-e^{x^2} x^2\right )} \]

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Rubi [A]  time = 0.17, antiderivative size = 21, normalized size of antiderivative = 1.11, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6706} \begin {gather*} e^{x^3+10 x^2-e^{x^2} x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(10*x^2 + x^3 - E^x^2*x^4)*(20*x + 3*x^2 + E^x^2*(-4*x^3 - 2*x^5)),x]

[Out]

E^(10*x^2 + x^3 - E^x^2*x^4)

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=e^{10 x^2+x^3-e^{x^2} x^4}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.42, size = 21, normalized size = 1.11 \begin {gather*} e^{10 x^2+x^3-e^{x^2} x^4} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(10*x^2 + x^3 - E^x^2*x^4)*(20*x + 3*x^2 + E^x^2*(-4*x^3 - 2*x^5)),x]

[Out]

E^(10*x^2 + x^3 - E^x^2*x^4)

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fricas [A]  time = 0.73, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (-x^{4} e^{\left (x^{2}\right )} + x^{3} + 10 \, x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^5-4*x^3)*exp(x^2)+3*x^2+20*x)*exp(-x^4*exp(x^2)+x^3+10*x^2),x, algorithm="fricas")

[Out]

e^(-x^4*e^(x^2) + x^3 + 10*x^2)

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giac [A]  time = 0.35, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (-x^{4} e^{\left (x^{2}\right )} + x^{3} + 10 \, x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^5-4*x^3)*exp(x^2)+3*x^2+20*x)*exp(-x^4*exp(x^2)+x^3+10*x^2),x, algorithm="giac")

[Out]

e^(-x^4*e^(x^2) + x^3 + 10*x^2)

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maple [A]  time = 0.04, size = 20, normalized size = 1.05

method	result	size
norman	\({\mathrm e}^{-x^{4} {\mathrm e}^{x^{2}}+x^{3}+10 x^{2}}\)	\(20\)
risch	\({\mathrm e}^{-x^{2} \left (x^{2} {\mathrm e}^{x^{2}}-x -10\right )}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-2*x^5-4*x^3)*exp(x^2)+3*x^2+20*x)*exp(-x^4*exp(x^2)+x^3+10*x^2),x,method=_RETURNVERBOSE)

[Out]

exp(-x^4*exp(x^2)+x^3+10*x^2)

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maxima [A]  time = 0.84, size = 19, normalized size = 1.00 \begin {gather*} e^{\left (-x^{4} e^{\left (x^{2}\right )} + x^{3} + 10 \, x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x^5-4*x^3)*exp(x^2)+3*x^2+20*x)*exp(-x^4*exp(x^2)+x^3+10*x^2),x, algorithm="maxima")

[Out]

e^(-x^4*e^(x^2) + x^3 + 10*x^2)

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mupad [B]  time = 0.31, size = 21, normalized size = 1.11 \begin {gather*} {\mathrm {e}}^{x^3}\,{\mathrm {e}}^{10\,x^2}\,{\mathrm {e}}^{-x^4\,{\mathrm {e}}^{x^2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(10*x^2 - x^4*exp(x^2) + x^3)*(20*x - exp(x^2)*(4*x^3 + 2*x^5) + 3*x^2),x)

[Out]

exp(x^3)*exp(10*x^2)*exp(-x^4*exp(x^2))

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sympy [A]  time = 0.29, size = 17, normalized size = 0.89 \begin {gather*} e^{- x^{4} e^{x^{2}} + x^{3} + 10 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-2*x**5-4*x**3)*exp(x**2)+3*x**2+20*x)*exp(-x**4*exp(x**2)+x**3+10*x**2),x)

[Out]

exp(-x**4*exp(x**2) + x**3 + 10*x**2)

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