Optimal. Leaf size=8 \[ \frac{a^x}{\log (a)} \]
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Rubi [A] time = 0.002335, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {2194} \[ \frac{a^x}{\log (a)} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin{align*} \int a^x \, dx &=\frac{a^x}{\log (a)}\\ \end{align*}
Mathematica [A] time = 0.0005207, size = 8, normalized size = 1. \[ \frac{a^x}{\log (a)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 9, normalized size = 1.1 \begin{align*}{\frac{{a}^{x}}{\ln \left ( a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.9221, size = 11, normalized size = 1.38 \begin{align*} \frac{a^{x}}{\log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.89986, size = 16, normalized size = 2. \begin{align*} \frac{a^{x}}{\log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.082901, size = 8, normalized size = 1. \begin{align*} \begin{cases} \frac{a^{x}}{\log{\left (a \right )}} & \text{for}\: \log{\left (a \right )} \neq 0 \\x & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04125, size = 11, normalized size = 1.38 \begin{align*} \frac{a^{x}}{\log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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