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

Optimal. Leaf size=16 \[ \frac {e^{x^2}}{2}-\log (-1+e) \]

________________________________________________________________________________________

Rubi [A]  time = 0.01, antiderivative size = 9, normalized size of antiderivative = 0.56, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2209} \begin {gather*} \frac {e^{x^2}}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^x^2/2

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} &=\frac {e^{x^2}}{2}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 9, normalized size = 0.56 \begin {gather*} \frac {e^{x^2}}{2} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

E^x^2/2

________________________________________________________________________________________

fricas [A]  time = 0.68, size = 6, normalized size = 0.38 \begin {gather*} \frac {1}{2} \, e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^(x^2)

________________________________________________________________________________________

giac [A]  time = 0.14, size = 6, normalized size = 0.38 \begin {gather*} \frac {1}{2} \, e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^(x^2)

________________________________________________________________________________________

maple [A]  time = 0.02, size = 7, normalized size = 0.44

method	result	size
gosper	\(\frac {{\mathrm e}^{x^{2}}}{2}\)	\(7\)
derivativedivides	\(\frac {{\mathrm e}^{x^{2}}}{2}\)	\(7\)
default	\(\frac {{\mathrm e}^{x^{2}}}{2}\)	\(7\)
norman	\(\frac {{\mathrm e}^{x^{2}}}{2}\)	\(7\)
risch	\(\frac {{\mathrm e}^{x^{2}}}{2}\)	\(7\)
meijerg	\(-\frac {1}{2}+\frac {{\mathrm e}^{x^{2}}}{2}\)	\(9\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*exp(x^2)

________________________________________________________________________________________

maxima [A]  time = 0.36, size = 6, normalized size = 0.38 \begin {gather*} \frac {1}{2} \, e^{\left (x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^(x^2)

________________________________________________________________________________________

mupad [B]  time = 0.02, size = 6, normalized size = 0.38 \begin {gather*} \frac {{\mathrm {e}}^{x^2}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x^2)/2

________________________________________________________________________________________

sympy [A]  time = 0.07, size = 5, normalized size = 0.31 \begin {gather*} \frac {e^{x^{2}}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x**2)/2

________________________________________________________________________________________