3.74.42 \(\int (3 x^2+3 e^{3-x^3} x^2) \, dx\)

Optimal. Leaf size=21 \[ -3+e^6-e^{3-x^3}+x^3+\log (5) \]

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Rubi [A]  time = 0.02, antiderivative size = 15, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {2209} \begin {gather*} x^3-e^{3-x^3} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3*x^2 + 3*E^(3 - x^3)*x^2,x]

[Out]

-E^(3 - x^3) + x^3

Rule 2209

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^(n_))*((e_.) + (f_.)*(x_))^(m_.), x_Symbol] :> Simp[((e + f*x)^n*
F^(a + b*(c + d*x)^n))/(b*f*n*(c + d*x)^n*Log[F]), x] /; FreeQ[{F, a, b, c, d, e, f, n}, x] && EqQ[m, n - 1] &
& EqQ[d*e - c*f, 0]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=x^3+3 \int e^{3-x^3} x^2 \, dx\\ &=-e^{3-x^3}+x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.02, size = 15, normalized size = 0.71 \begin {gather*} -e^{3-x^3}+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[3*x^2 + 3*E^(3 - x^3)*x^2,x]

[Out]

-E^(3 - x^3) + x^3

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fricas [A]  time = 0.63, size = 14, normalized size = 0.67 \begin {gather*} x^{3} - e^{\left (-x^{3} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^3 - e^(-x^3 + 3)

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giac [A]  time = 0.13, size = 14, normalized size = 0.67 \begin {gather*} x^{3} - e^{\left (-x^{3} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^3 - e^(-x^3 + 3)

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maple [A]  time = 0.02, size = 15, normalized size = 0.71

method	result	size
default	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)
norman	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)
risch	\(x^{3}-{\mathrm e}^{-x^{3}+3}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2*exp(-x^3+3)+3*x^2,x,method=_RETURNVERBOSE)

[Out]

x^3-exp(-x^3+3)

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maxima [A]  time = 0.36, size = 14, normalized size = 0.67 \begin {gather*} x^{3} - e^{\left (-x^{3} + 3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

x^3 - e^(-x^3 + 3)

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mupad [B]  time = 4.53, size = 14, normalized size = 0.67 \begin {gather*} x^3-{\mathrm {e}}^{3-x^3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3*x^2*exp(3 - x^3) + 3*x^2,x)

[Out]

x^3 - exp(3 - x^3)

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sympy [A]  time = 0.09, size = 8, normalized size = 0.38 \begin {gather*} x^{3} - e^{3 - x^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(3*x**2*exp(-x**3+3)+3*x**2,x)

[Out]

x**3 - exp(3 - x**3)

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