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

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

[Out]

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

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Rubi [A]  time = 0.01, antiderivative size = 11, 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} \[ \frac {e^{x^2+1}}{2} \]

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*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 1.00 \[ \frac {e^{x^2+1}}{2} \]

Antiderivative was successfully verified.

[In]

Integrate[E^(1 + x^2)*x,x]

[Out]

E^(1 + x^2)/2

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fricas [A]  time = 0.39, size = 8, normalized size = 0.73 \[ \frac {1}{2} \, e^{\left (x^{2} + 1\right )} \]

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)

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giac [A]  time = 0.19, size = 8, normalized size = 0.73 \[ \frac {1}{2} \, e^{\left (x^{2} + 1\right )} \]

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)

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maple [A]  time = 0.02, size = 9, normalized size = 0.82 \[ \frac {{\mathrm e}^{x^{2}+1}}{2} \]

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)

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maxima [A]  time = 0.91, size = 8, normalized size = 0.73 \[ \frac {1}{2} \, e^{\left (x^{2} + 1\right )} \]

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)

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mupad [B]  time = 0.05, size = 8, normalized size = 0.73 \[ \frac {{\mathrm {e}}^{x^2}\,\mathrm {e}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x*exp(x^2 + 1),x)

[Out]

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

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sympy [A]  time = 0.08, size = 7, normalized size = 0.64 \[ \frac {e^{x^{2} + 1}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(x**2 + 1)/2

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