Optimal. Leaf size=26 \[ (\log (a)+\log (b)) \text{ExpIntegralEi}(x (\log (a)+\log (b)))-\frac{a^x b^x}{x} \]
[Out]
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Rubi [A] time = 0.0952695, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.3 \[ (\log (a)+\log (b)) \text{ExpIntegralEi}(x (\log (a)+\log (b)))-\frac{a^x b^x}{x} \]
Antiderivative was successfully verified.
[In] Int[(a^x*b^x)/x^2,x]
[Out]
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Rubi in Sympy [A] time = 10.9402, size = 27, normalized size = 1.04 \[ \left (\log{\left (a \right )} + \log{\left (b \right )}\right ) \operatorname{Ei}{\left (x \left (\log{\left (a \right )} + \log{\left (b \right )}\right ) \right )} - \frac{e^{x \left (\log{\left (a \right )} + \log{\left (b \right )}\right )}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(a**x*b**x/x**2,x)
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Mathematica [A] time = 0.0446168, size = 0, normalized size = 0. \[ \int \frac{a^x b^x}{x^2} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[(a^x*b^x)/x^2,x]
[Out]
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Maple [C] time = 0.046, size = 160, normalized size = 6.2 \[ -\ln \left ( b \right ) \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) \left ({\frac{1}{\ln \left ( b \right ) x} \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) ^{-1}}+1-\ln \left ( x \right ) -i\pi -\ln \left ( \ln \left ( b \right ) \right ) -\ln \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) -{\frac{1}{2\,\ln \left ( b \right ) x} \left ( 2\,x\ln \left ( b \right ) \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) +2 \right ) \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) ^{-1}}+{\frac{1}{\ln \left ( b \right ) x}{{\rm e}^{x\ln \left ( b \right ) \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) }} \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) ^{-1}}+\ln \left ( -x\ln \left ( b \right ) \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) \right ) +{\it Ei} \left ( 1,-x\ln \left ( b \right ) \left ( 1+{\frac{\ln \left ( a \right ) }{\ln \left ( b \right ) }} \right ) \right ) \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(a^x*b^x/x^2,x)
[Out]
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Maxima [A] time = 0.818246, size = 22, normalized size = 0.85 \[{\left (\log \left (a\right ) + \log \left (b\right )\right )} \Gamma \left (-1, -x{\left (\log \left (a\right ) + \log \left (b\right )\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a^x*b^x/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.247043, size = 46, normalized size = 1.77 \[ -\frac{a^{x} b^{x} -{\left (x \log \left (a\right ) + x \log \left (b\right )\right )}{\rm Ei}\left (x \log \left (a\right ) + x \log \left (b\right )\right )}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a^x*b^x/x^2,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{a^{x} b^{x}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a**x*b**x/x**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{a^{x} b^{x}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(a^x*b^x/x^2,x, algorithm="giac")
[Out]