Integrand size = 3, antiderivative size = 8 \[ \int b^x \, dx=\frac {b^x}{\log (b)} \]
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Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2225} \[ \int b^x \, dx=\frac {b^x}{\log (b)} \]
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Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {b^x}{\log (b)} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int b^x \, dx=\frac {b^x}{\log (b)} \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.12
method | result | size |
gosper | \(\frac {b^{x}}{\ln \left (b \right )}\) | \(9\) |
derivativedivides | \(\frac {b^{x}}{\ln \left (b \right )}\) | \(9\) |
default | \(\frac {b^{x}}{\ln \left (b \right )}\) | \(9\) |
risch | \(\frac {b^{x}}{\ln \left (b \right )}\) | \(9\) |
parallelrisch | \(\frac {b^{x}}{\ln \left (b \right )}\) | \(9\) |
norman | \(\frac {{\mathrm e}^{x \ln \left (b \right )}}{\ln \left (b \right )}\) | \(11\) |
meijerg | \(-\frac {1-{\mathrm e}^{x \ln \left (b \right )}}{\ln \left (b \right )}\) | \(16\) |
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Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int b^x \, dx=\frac {b^{x}}{\log \left (b\right )} \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int b^x \, dx=\begin {cases} \frac {b^{x}}{\log {\left (b \right )}} & \text {for}\: \log {\left (b \right )} \neq 0 \\x & \text {otherwise} \end {cases} \]
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Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int b^x \, dx=\frac {b^{x}}{\log \left (b\right )} \]
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Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int b^x \, dx=\frac {b^{x}}{\log \left (b\right )} \]
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Time = 0.17 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int b^x \, dx=\frac {b^x}{\ln \left (b\right )} \]
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