Optimal. Leaf size=28 \[ \frac{a^{k x}}{k \log (a)}-\frac{a^{l x}}{l \log (a)} \]
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Rubi [A] time = 0.0083801, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, 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 = 0.0061269, size = 28, 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 = 0.001, size = 29, 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 = 0.934184, size = 38, normalized size = 1.36 \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 = 1.87292, size = 53, 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 = 0.287002, size = 29, normalized size = 1.04 \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 = 1.12463, size = 38, normalized size = 1.36 \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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