\(\int e^{1+x^3} x^2 \, dx\) [670]

Optimal result

Integrand size = 11, antiderivative size = 11 \[ \int e^{1+x^3} x^2 \, dx=\frac {e^{1+x^3}}{3} \]

[Out]

1/3*exp(x^3+1)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2240} \[ \int e^{1+x^3} x^2 \, dx=\frac {e^{x^3+1}}{3} \]

[In]

Int[E^(1 + x^3)*x^2,x]

[Out]

E^(1 + 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^{1+x^3}}{3} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int e^{1+x^3} x^2 \, dx=\frac {e^{1+x^3}}{3} \]

[In]

Integrate[E^(1 + x^3)*x^2,x]

[Out]

E^(1 + x^3)/3

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82

method	result	size
gosper	\(\frac {{\mathrm e}^{x^{3}+1}}{3}\)	\(9\)
derivativedivides	\(\frac {{\mathrm e}^{x^{3}+1}}{3}\)	\(9\)
default	\(\frac {{\mathrm e}^{x^{3}+1}}{3}\)	\(9\)
norman	\(\frac {{\mathrm e}^{x^{3}+1}}{3}\)	\(9\)
parallelrisch	\(\frac {{\mathrm e}^{x^{3}+1}}{3}\)	\(9\)
meijerg	\(-\frac {{\mathrm e} \left (1-{\mathrm e}^{x^{3}}\right )}{3}\)	\(13\)
risch	\(\frac {{\mathrm e}^{\left (1+x \right ) \left (x^{2}-x +1\right )}}{3}\)	\(16\)

[In]

int(exp(x^3+1)*x^2,x,method=_RETURNVERBOSE)

[Out]

1/3*exp(x^3+1)

Fricas [A] (verification not implemented)

none

Time = 0.33 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^3} x^2 \, dx=\frac {1}{3} \, e^{\left (x^{3} + 1\right )} \]

[In]

integrate(exp(x^3+1)*x^2,x, algorithm="fricas")

[Out]

1/3*e^(x^3 + 1)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int e^{1+x^3} x^2 \, dx=\frac {e^{x^{3} + 1}}{3} \]

[In]

integrate(exp(x**3+1)*x**2,x)

[Out]

exp(x**3 + 1)/3

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^3} x^2 \, dx=\frac {1}{3} \, e^{\left (x^{3} + 1\right )} \]

[In]

integrate(exp(x^3+1)*x^2,x, algorithm="maxima")

[Out]

1/3*e^(x^3 + 1)

Giac [A] (verification not implemented)

none

Time = 0.30 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^3} x^2 \, dx=\frac {1}{3} \, e^{\left (x^{3} + 1\right )} \]

[In]

integrate(exp(x^3+1)*x^2,x, algorithm="giac")

[Out]

1/3*e^(x^3 + 1)

Mupad [B] (verification not implemented)

Time = 0.21 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int e^{1+x^3} x^2 \, dx=\frac {{\mathrm {e}}^{x^3}\,\mathrm {e}}{3} \]

[In]

int(x^2*exp(x^3 + 1),x)

[Out]

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