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

Optimal. Leaf size=9 \[ \frac {e^{x^3}}{3} \]

[Out]

1/3*exp(x^3)

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Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2209} \[ \frac {e^{x^3}}{3} \]

Antiderivative was successfully verified.

[In]

Int[E^x^3*x^2,x]

[Out]

E^x^3/3

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

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Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \[ \frac {e^{x^3}}{3} \]

Antiderivative was successfully verified.

[In]

Integrate[E^x^3*x^2,x]

[Out]

E^x^3/3

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fricas [A]  time = 0.41, size = 6, normalized size = 0.67 \[ \frac {1}{3} \, e^{\left (x^{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*e^(x^3)

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giac [A]  time = 0.01, size = 6, normalized size = 0.67 \[ \frac {1}{3} \, e^{\left (x^{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*e^(x^3)

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maple [A]  time = 0.00, size = 7, normalized size = 0.78 \[ \frac {{\mathrm e}^{x^{3}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*exp(x^3)

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maxima [A]  time = 0.49, size = 6, normalized size = 0.67 \[ \frac {1}{3} \, e^{\left (x^{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3*e^(x^3)

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mupad [B]  time = 0.08, size = 6, normalized size = 0.67 \[ \frac {{\mathrm {e}}^{x^3}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x^3)/3

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sympy [A]  time = 0.09, size = 5, normalized size = 0.56 \[ \frac {e^{x^{3}}}{3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x**3)/3

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