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

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 = 0.0168679, 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 \[ \frac{3^{x^2+1}}{2 \log (3)} \]

Antiderivative was successfully verified.

[In]  Int[3^(1 + x^2)*x,x]

[Out]

3^(1 + x^2)/(2*Log[3])

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Rubi in Sympy [A]  time = 2.03353, size = 10, normalized size = 0.67 \[ \frac{3^{x^{2} + 1}}{2 \log{\left (3 \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(3**(x**2+1)*x,x)

[Out]

3**(x**2 + 1)/(2*log(3))

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Mathematica [A]  time = 0.00321775, 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 = 0.012, size = 14, normalized size = 0.9 \[{\frac{{3}^{{x}^{2}+1}}{2\,\ln \left ( 3 \right ) }} \]

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 = 0.752667, size = 18, normalized size = 1.2 \[ \frac{3^{x^{2} + 1}}{2 \, \log \left (3\right )} \]

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 = 0.305054, size = 18, normalized size = 1.2 \[ \frac{3^{x^{2} + 1}}{2 \, \log \left (3\right )} \]

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 = 0.078885, size = 10, normalized size = 0.67 \[ \frac{3^{x^{2} + 1}}{2 \log{\left (3 \right )}} \]

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/XCAS [A]  time = 0.227671, size = 18, normalized size = 1.2 \[ \frac{3^{x^{2} + 1}}{2 \,{\rm ln}\left (3\right )} \]

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)/ln(3)