\(\int e^{x^3} x^2 \, dx\) [68]

Optimal result

Integrand size = 9, antiderivative size = 9 \[ \int e^{x^3} x^2 \, dx=\frac {e^{x^3}}{3} \]

[Out]

1/3*exp(x^3)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2240} \[ \int e^{x^3} x^2 \, dx=\frac {e^{x^3}}{3} \]

[In]

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

[Out]

E^x^3/3

Rule 2240

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*} \text {integral}& = \frac {e^{x^3}}{3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int e^{x^3} x^2 \, dx=\frac {e^{x^3}}{3} \]

[In]

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

[Out]

E^x^3/3

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78

method	result	size
gosper	\(\frac {{\mathrm e}^{x^{3}}}{3}\)	\(7\)
derivativedivides	\(\frac {{\mathrm e}^{x^{3}}}{3}\)	\(7\)
default	\(\frac {{\mathrm e}^{x^{3}}}{3}\)	\(7\)
norman	\(\frac {{\mathrm e}^{x^{3}}}{3}\)	\(7\)
risch	\(\frac {{\mathrm e}^{x^{3}}}{3}\)	\(7\)
parallelrisch	\(\frac {{\mathrm e}^{x^{3}}}{3}\)	\(7\)
meijerg	\(-\frac {1}{3}+\frac {{\mathrm e}^{x^{3}}}{3}\)	\(9\)

[In]

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

[Out]

1/3*exp(x^3)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int e^{x^3} x^2 \, dx=\frac {1}{3} \, e^{\left (x^{3}\right )} \]

[In]

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

[Out]

1/3*e^(x^3)

Sympy [A] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int e^{x^3} x^2 \, dx=\frac {e^{x^{3}}}{3} \]

[In]

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

[Out]

exp(x**3)/3

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int e^{x^3} x^2 \, dx=\frac {1}{3} \, e^{\left (x^{3}\right )} \]

[In]

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

[Out]

1/3*e^(x^3)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int e^{x^3} x^2 \, dx=\frac {1}{3} \, e^{\left (x^{3}\right )} \]

[In]

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

[Out]

1/3*e^(x^3)

Mupad [B] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int e^{x^3} x^2 \, dx=\frac {{\mathrm {e}}^{x^3}}{3} \]

[In]

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

[Out]

exp(x^3)/3