Integrand size = 9, antiderivative size = 15 \[ \int 3^{1+x^2} x \, dx=\frac {3^{1+x^2}}{2 \log (3)} \]
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Time = 0.01 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2240} \[ \int 3^{1+x^2} x \, dx=\frac {3^{x^2+1}}{2 \log (3)} \]
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Rule 2240
Rubi steps \begin{align*} \text {integral}& = \frac {3^{1+x^2}}{2 \log (3)} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int 3^{1+x^2} x \, dx=\frac {3^{1+x^2}}{\log (9)} \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80
method | result | size |
derivativedivides | \(\frac {3 \,3^{x^{2}}}{2 \ln \left (3\right )}\) | \(12\) |
default | \(\frac {3 \,3^{x^{2}}}{2 \ln \left (3\right )}\) | \(12\) |
gosper | \(\frac {3^{x^{2}+1}}{2 \ln \left (3\right )}\) | \(14\) |
risch | \(\frac {3^{x^{2}+1}}{2 \ln \left (3\right )}\) | \(14\) |
parallelrisch | \(\frac {3^{x^{2}+1}}{2 \ln \left (3\right )}\) | \(14\) |
norman | \(\frac {{\mathrm e}^{\left (x^{2}+1\right ) \ln \left (3\right )}}{2 \ln \left (3\right )}\) | \(16\) |
meijerg | \(-\frac {3 \left (1-{\mathrm e}^{\ln \left (3\right ) x^{2}}\right )}{2 \ln \left (3\right )}\) | \(18\) |
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none
Time = 0.30 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int 3^{1+x^2} x \, dx=\frac {3^{x^{2} + 1}}{2 \, \log \left (3\right )} \]
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Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int 3^{1+x^2} x \, dx=\frac {3^{x^{2} + 1}}{2 \log {\left (3 \right )}} \]
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none
Time = 0.19 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int 3^{1+x^2} x \, dx=\frac {3^{x^{2} + 1}}{2 \, \log \left (3\right )} \]
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none
Time = 0.31 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int 3^{1+x^2} x \, dx=\frac {3^{x^{2} + 1}}{2 \, \log \left (3\right )} \]
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Time = 0.25 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int 3^{1+x^2} x \, dx=\frac {3\,3^{x^2}}{2\,\ln \left (3\right )} \]
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