Optimal. Leaf size=49 \[ x f^{a+\frac{b}{x^2}}-\sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0605577, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ x f^{a+\frac{b}{x^2}}-\sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right ) \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.37912, size = 44, normalized size = 0.9 \[ - \sqrt{\pi } \sqrt{b} f^{a} \sqrt{\log{\left (f \right )}} \operatorname{erfi}{\left (\frac{\sqrt{b} \sqrt{\log{\left (f \right )}}}{x} \right )} + f^{a + \frac{b}{x^{2}}} x \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x**2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0131193, size = 49, normalized size = 1. \[ x f^{a+\frac{b}{x^2}}-\sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.021, size = 44, normalized size = 0.9 \[{f}^{a}{f}^{{\frac{b}{{x}^{2}}}}x-{{f}^{a}\ln \left ( f \right ) b\sqrt{\pi }{\it Erf} \left ({\frac{1}{x}\sqrt{-b\ln \left ( f \right ) }} \right ){\frac{1}{\sqrt{-b\ln \left ( f \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x^2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.912201, size = 68, normalized size = 1.39 \[ f^{a} f^{\frac{b}{x^{2}}} x - \frac{\sqrt{\pi } b f^{a}{\left (\operatorname{erf}\left (\sqrt{-\frac{b \log \left (f\right )}{x^{2}}}\right ) - 1\right )} \log \left (f\right )}{x \sqrt{-\frac{b \log \left (f\right )}{x^{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.269228, size = 74, normalized size = 1.51 \[ -\frac{\sqrt{\pi } b f^{a} \operatorname{erf}\left (\frac{\sqrt{-b \log \left (f\right )}}{x}\right ) \log \left (f\right ) - \sqrt{-b \log \left (f\right )} f^{\frac{a x^{2} + b}{x^{2}}} x}{\sqrt{-b \log \left (f\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + \frac{b}{x^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x**2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + \frac{b}{x^{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2),x, algorithm="giac")
[Out]