3.8.37 \(\int 3^{1+x^2} x \, dx\) [737]

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

[Out]

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

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Rubi [A]
time = 0.01, antiderivative size = 15, 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 = {2240} \begin {gather*} \frac {3^{x^2+1}}{2 \log (3)} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[3^(1 + x^2)*x,x]

[Out]

3^(1 + x^2)/(2*Log[3])

Rule 2240

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*}

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Mathematica [A]
time = 0.03, size = 12, normalized size = 0.80 \begin {gather*} \frac {3^{1+x^2}}{\log (9)} \end {gather*}

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 = 0.02, size = 14, normalized size = 0.93

method	result	size
gosper	\(\frac {3^{x^{2}+1}}{2 \ln \left (3\right )}\)	\(14\)
derivativedivides	\(\frac {3^{x^{2}+1}}{2 \ln \left (3\right )}\)	\(14\)
default	\(\frac {3^{x^{2}+1}}{2 \ln \left (3\right )}\)	\(14\)
risch	\(\frac {3^{x^{2}+1}}{2 \ln \left (3\right )}\)	\(14\)
norman	\(\frac {{\mathrm e}^{\left (x^{2}+1\right ) \ln \left (3\right )}}{2 \ln \left (3\right )}\)	\(16\)
meijerg	\(-\frac {3 \left (1-{\mathrm e}^{\ln \left (3\right ) x^{2}}\right )}{2 \ln \left (3\right )}\)	\(18\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3^(x^2+1)*x,x,method=_RETURNVERBOSE)

[Out]

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

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Maxima [A]
time = 0.29, size = 13, normalized size = 0.87 \begin {gather*} \frac {3^{x^{2} + 1}}{2 \, \log \left (3\right )} \end {gather*}

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 = 0.35, size = 13, normalized size = 0.87 \begin {gather*} \frac {3^{x^{2} + 1}}{2 \, \log \left (3\right )} \end {gather*}

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 = 0.03, size = 10, normalized size = 0.67 \begin {gather*} \frac {3^{x^{2} + 1}}{2 \log {\left (3 \right )}} \end {gather*}

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 = 4.13, size = 13, normalized size = 0.87 \begin {gather*} \frac {3^{x^{2} + 1}}{2 \, \log \left (3\right )} \end {gather*}

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)

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Mupad [B]
time = 3.50, size = 11, normalized size = 0.73 \begin {gather*} \frac {3\,3^{x^2}}{2\,\ln \left (3\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(3^(x^2 + 1)*x,x)

[Out]

(3*3^(x^2))/(2*log(3))

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