Optimal. Leaf size=15 \[ \frac{a^{m x}}{m \log (a)}+x \]
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Rubi [A] time = 0.0055083, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {2194} \[ \frac{a^{m x}}{m \log (a)}+x \]
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 = 0.0038371, size = 15, normalized size = 1. \[ \frac{a^{m x}}{m \log (a)}+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 16, 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 = 0.923701, size = 20, normalized size = 1.33 \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 = 1.82672, size = 47, normalized size = 3.13 \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 = 0.087906, size = 15, normalized size = 1. \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 = 1.12403, size = 20, normalized size = 1.33 \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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