Optimal. Leaf size=16 \[ x-\frac {a^{m x}}{m \log (a)} \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ x-\frac {a^{m x}}{m \log (a)} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (1-a^{m x}\right ) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.98, size = 21, normalized size = 1.31 \[ \frac {m x \log \relax (a) - a^{m x}}{m \log \relax (a)} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.59, size = 16, normalized size = 1.00 \[ x - \frac {a^{m x}}{m \log \relax (a)} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 1.06
method | result | size |
default | \(x -\frac {a^{m x}}{m \ln \relax (a )}\) | \(17\) |
risch | \(x -\frac {a^{m x}}{m \ln \relax (a )}\) | \(17\) |
norman | \(x -\frac {{\mathrm e}^{m x \ln \relax (a )}}{m \ln \relax (a )}\) | \(18\) |
derivativedivides | \(\frac {-a^{m x}+\ln \left (a^{m x}\right )}{m \ln \relax (a )}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 16, normalized size = 1.00 \[ x - \frac {a^{m x}}{m \log \relax (a)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.30, size = 16, normalized size = 1.00 \[ x-\frac {a^{m\,x}}{m\,\ln \relax (a)} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 19, normalized size = 1.19 \[ x + \begin {cases} - \frac {a^{m x}}{m \log {\relax (a )}} & \text {for}\: m \log {\relax (a )} \neq 0 \\- x & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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