Optimal. Leaf size=15 \[ -\frac{1}{2} f^a \text{ExpIntegralEi}\left (\frac{b \log (f)}{x^2}\right ) \]
[Out]
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Rubi [A] time = 0.0352925, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{1}{2} f^a \text{ExpIntegralEi}\left (\frac{b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x^2)/x,x]
[Out]
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Rubi in Sympy [A] time = 3.04652, size = 15, normalized size = 1. \[ - \frac{f^{a} \operatorname{Ei}{\left (\frac{b \log{\left (f \right )}}{x^{2}} \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x**2)/x,x)
[Out]
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Mathematica [A] time = 0.00447528, size = 15, normalized size = 1. \[ -\frac{1}{2} f^a \text{ExpIntegralEi}\left (\frac{b \log (f)}{x^2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x^2)/x,x]
[Out]
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Maple [A] time = 0.019, size = 16, normalized size = 1.1 \[{\frac{{f}^{a}}{2}{\it Ei} \left ( 1,-{\frac{b\ln \left ( f \right ) }{{x}^{2}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x^2)/x,x)
[Out]
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Maxima [A] time = 0.933301, size = 18, normalized size = 1.2 \[ -\frac{1}{2} \, f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)/x,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244006, size = 18, normalized size = 1.2 \[ -\frac{1}{2} \, f^{a}{\rm Ei}\left (\frac{b \log \left (f\right )}{x^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)/x,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + \frac{b}{x^{2}}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x**2)/x,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + \frac{b}{x^{2}}}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)/x,x, algorithm="giac")
[Out]