Optimal. Leaf size=8 \[ \text {Ei}(x (\log (a)+\log (b))) \]
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Rubi [A] time = 0.04, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2287, 2178} \[ \text {Ei}(x (\log (a)+\log (b))) \]
Antiderivative was successfully verified.
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Rule 2178
Rule 2287
Rubi steps
\begin {align*} \int \frac {a^x b^x}{x} \, dx &=\int \frac {e^{x (\log (a)+\log (b))}}{x} \, dx\\ &=\text {Ei}(x (\log (a)+\log (b)))\\ \end {align*}
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Mathematica [A] time = 0.01, size = 10, normalized size = 1.25 \[ \text {Ei}(x \log (a)+x \log (b)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 10, normalized size = 1.25 \[ {\rm Ei}\left (x \log \relax (a) + x \log \relax (b)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {a^{x} b^{x}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.06, size = 56, normalized size = 7.00 \[ -\Ei \left (1, -\left (\frac {\ln \relax (a )}{\ln \relax (b )}+1\right ) x \ln \relax (b )\right )+\ln \relax (x )-\ln \left (-\left (\frac {\ln \relax (a )}{\ln \relax (b )}+1\right ) x \ln \relax (b )\right )+\ln \left (\frac {\ln \relax (a )}{\ln \relax (b )}+1\right )+\ln \left (\ln \relax (b )\right )+i \pi \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.34, size = 8, normalized size = 1.00 \[ {\rm Ei}\left (x {\left (\log \relax (a) + \log \relax (b)\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 8, normalized size = 1.00 \[ \mathrm {ei}\left (x\,\left (\ln \relax (a)+\ln \relax (b)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {a^{x} b^{x}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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