3.737 \(\int 3^{1+x^2} x \, dx\)

Optimal. Leaf size=15 \[ \frac{3^{x^2+1}}{2 \log (3)} \]

[Out]

3^(1 + x^2)/(2*Log[3])

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Rubi [A]  time = 0.0094084, antiderivative size = 15, 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} \[ \frac{3^{x^2+1}}{2 \log (3)} \]

Antiderivative was successfully verified.

[In]

Int[3^(1 + x^2)*x,x]

[Out]

3^(1 + x^2)/(2*Log[3])

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 3^{1+x^2} x \, dx &=\frac{3^{1+x^2}}{2 \log (3)}\\ \end{align*}

Mathematica [A]  time = 0.0020117, size = 12, normalized size = 0.8 \[ \frac{3^{x^2+1}}{\log (9)} \]

Antiderivative was successfully verified.

[In]

Integrate[3^(1 + x^2)*x,x]

[Out]

3^(1 + x^2)/Log[9]

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Maple [A]  time = 0.024, size = 14, normalized size = 0.9 \begin{align*}{\frac{{3}^{{x}^{2}+1}}{2\,\ln \left ( 3 \right ) }} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3^(x^2+1)*x,x)

[Out]

1/2*3^(x^2+1)/ln(3)

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Maxima [A]  time = 0.96544, size = 18, normalized size = 1.2 \begin{align*} \frac{3^{x^{2} + 1}}{2 \, \log \left (3\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*3^(x^2 + 1)/log(3)

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Fricas [A]  time = 0.761449, size = 32, normalized size = 2.13 \begin{align*} \frac{3^{x^{2} + 1}}{2 \, \log \left (3\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*3^(x^2 + 1)/log(3)

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Sympy [A]  time = 0.093969, size = 10, normalized size = 0.67 \begin{align*} \frac{3^{x^{2} + 1}}{2 \log{\left (3 \right )}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

3**(x**2 + 1)/(2*log(3))

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Giac [A]  time = 1.19112, size = 18, normalized size = 1.2 \begin{align*} \frac{3^{x^{2} + 1}}{2 \, \log \left (3\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/2*3^(x^2 + 1)/log(3)