Optimal. Leaf size=27 \[ \frac{a^{k x}}{k \log (a)}+\frac{a^{l x}}{l \log (a)} \]
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Rubi [A] time = 0.010812, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {2194} \[ \frac{a^{k x}}{k \log (a)}+\frac{a^{l x}}{l \log (a)} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin{align*} \int \left (a^{k x}+a^{l x}\right ) \, dx &=\int a^{k x} \, dx+\int a^{l x} \, dx\\ &=\frac{a^{k x}}{k \log (a)}+\frac{a^{l x}}{l \log (a)}\\ \end{align*}
Mathematica [A] time = 0.0058437, size = 27, normalized size = 1. \[ \frac{a^{k x}}{k \log (a)}+\frac{a^{l x}}{l \log (a)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 28, normalized size = 1. \begin{align*}{\frac{{a}^{kx}}{k\ln \left ( a \right ) }}+{\frac{{a}^{lx}}{l\ln \left ( a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.948154, size = 36, normalized size = 1.33 \begin{align*} \frac{a^{k x}}{k \log \left (a\right )} + \frac{a^{l x}}{l \log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.76971, size = 51, normalized size = 1.89 \begin{align*} \frac{a^{l x} k + a^{k x} l}{k l \log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.286201, size = 29, normalized size = 1.07 \begin{align*} \begin{cases} \frac{a^{k x}}{k \log{\left (a \right )}} & \text{for}\: k \log{\left (a \right )} \neq 0 \\x & \text{otherwise} \end{cases} + \begin{cases} \frac{a^{l x}}{l \log{\left (a \right )}} & \text{for}\: l \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 = 1.06494, size = 36, normalized size = 1.33 \begin{align*} \frac{a^{k x}}{k \log \left (a\right )} + \frac{a^{l x}}{l \log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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