Optimal. Leaf size=16 \[ x-\frac{a^{m x}}{m \log (a)} \]
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Rubi [A] time = 0.0050012, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {2194} \[ x-\frac{a^{m x}}{m \log (a)} \]
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin{align*} \int \left (1-a^{m x}\right ) \, dx &=x-\int a^{m x} \, dx\\ &=x-\frac{a^{m x}}{m \log (a)}\\ \end{align*}
Mathematica [A] time = 0.0042407, size = 16, normalized size = 1. \[ x-\frac{a^{m x}}{m \log (a)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 17, normalized size = 1.1 \begin{align*} x-{\frac{{a}^{mx}}{m\ln \left ( a \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926793, size = 22, normalized size = 1.38 \begin{align*} x - \frac{a^{m x}}{m \log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.83819, size = 47, normalized size = 2.94 \begin{align*} \frac{m x \log \left (a\right ) - a^{m x}}{m \log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.090836, size = 19, normalized size = 1.19 \begin{align*} x + \begin{cases} - \frac{a^{m x}}{m \log{\left (a \right )}} & \text{for}\: m \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 = 1.16075, size = 22, normalized size = 1.38 \begin{align*} x - \frac{a^{m x}}{m \log \left (a\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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