3.669 \(\int e^{1+x^2} x \, dx\)

Optimal. Leaf size=11 \[ \frac{e^{x^2+1}}{2} \]

[Out]

E^(1 + x^2)/2

________________________________________________________________________________________

Rubi [A]  time = 0.008696, antiderivative size = 11, normalized size of antiderivative = 1., 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} \[ \frac{e^{x^2+1}}{2} \]

Antiderivative was successfully verified.

[In]

Int[E^(1 + x^2)*x,x]

[Out]

E^(1 + 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{align*} \int e^{1+x^2} x \, dx &=\frac{e^{1+x^2}}{2}\\ \end{align*}

Mathematica [A]  time = 0.0015886, size = 11, normalized size = 1. \[ \frac{e^{x^2+1}}{2} \]

Antiderivative was successfully verified.

[In]

Integrate[E^(1 + x^2)*x,x]

[Out]

E^(1 + x^2)/2

________________________________________________________________________________________

Maple [A]  time = 0.019, size = 9, normalized size = 0.8 \begin{align*}{\frac{{{\rm e}^{{x}^{2}+1}}}{2}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(x^2+1)*x,x)

[Out]

1/2*exp(x^2+1)

________________________________________________________________________________________

Maxima [A]  time = 0.968426, size = 11, normalized size = 1. \begin{align*} \frac{1}{2} \, e^{\left (x^{2} + 1\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^(x^2 + 1)

________________________________________________________________________________________

Fricas [A]  time = 0.86566, size = 23, normalized size = 2.09 \begin{align*} \frac{1}{2} \, e^{\left (x^{2} + 1\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^(x^2 + 1)

________________________________________________________________________________________

Sympy [A]  time = 0.0847, size = 7, normalized size = 0.64 \begin{align*} \frac{e^{x^{2} + 1}}{2} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x**2 + 1)/2

________________________________________________________________________________________

Giac [A]  time = 1.26829, size = 11, normalized size = 1. \begin{align*} \frac{1}{2} \, e^{\left (x^{2} + 1\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*e^(x^2 + 1)