3.114 \(\int e^{4 x^3} x^2 \, dx\)

Optimal. Leaf size=11 \[ \frac{e^{4 x^3}}{12} \]

[Out]

E^(4*x^3)/12

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Rubi [A]  time = 0.0143383, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {2209} \[ \frac{e^{4 x^3}}{12} \]

Antiderivative was successfully verified.

[In]

Int[E^(4*x^3)*x^2,x]

[Out]

E^(4*x^3)/12

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{align*} \int e^{4 x^3} x^2 \, dx &=\frac{e^{4 x^3}}{12}\\ \end{align*}

Mathematica [A]  time = 0.001619, size = 11, normalized size = 1. \[ \frac{e^{4 x^3}}{12} \]

Antiderivative was successfully verified.

[In]

Integrate[E^(4*x^3)*x^2,x]

[Out]

E^(4*x^3)/12

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Maple [A]  time = 0.003, size = 9, normalized size = 0.8 \begin{align*}{\frac{{{\rm e}^{4\,{x}^{3}}}}{12}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(4*x^3)*x^2,x)

[Out]

1/12*exp(4*x^3)

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Maxima [A]  time = 1.18386, size = 11, normalized size = 1. \begin{align*} \frac{1}{12} \, e^{\left (4 \, x^{3}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(4*x^3)*x^2,x, algorithm="maxima")

[Out]

1/12*e^(4*x^3)

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Fricas [A]  time = 1.79657, size = 22, normalized size = 2. \begin{align*} \frac{1}{12} \, e^{\left (4 \, x^{3}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(4*x^3)*x^2,x, algorithm="fricas")

[Out]

1/12*e^(4*x^3)

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Sympy [A]  time = 0.084682, size = 7, normalized size = 0.64 \begin{align*} \frac{e^{4 x^{3}}}{12} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(4*x**3)*x**2,x)

[Out]

exp(4*x**3)/12

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Giac [A]  time = 1.24131, size = 11, normalized size = 1. \begin{align*} \frac{1}{12} \, e^{\left (4 \, x^{3}\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(4*x^3)*x^2,x, algorithm="giac")

[Out]

1/12*e^(4*x^3)