Optimal. Leaf size=49 \[ \sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{Erfi}\left (\sqrt{b} x \sqrt{\log (f)}\right )-\frac{f^{a+b x^2}}{x} \]
[Out]
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Rubi [A] time = 0.0574331, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{Erfi}\left (\sqrt{b} x \sqrt{\log (f)}\right )-\frac{f^{a+b x^2}}{x} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^2)/x^2,x]
[Out]
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Rubi in Sympy [A] time = 5.25911, size = 44, normalized size = 0.9 \[ \sqrt{\pi } \sqrt{b} f^{a} \sqrt{\log{\left (f \right )}} \operatorname{erfi}{\left (\sqrt{b} x \sqrt{\log{\left (f \right )}} \right )} - \frac{f^{a + b x^{2}}}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(b*x**2+a)/x**2,x)
[Out]
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Mathematica [A] time = 0.0234826, size = 49, normalized size = 1. \[ \sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{Erfi}\left (\sqrt{b} x \sqrt{\log (f)}\right )-\frac{f^{a+b x^2}}{x} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^2)/x^2,x]
[Out]
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Maple [A] time = 0.026, size = 44, normalized size = 0.9 \[ -{\frac{{f}^{a}{f}^{b{x}^{2}}}{x}}+{{f}^{a}\ln \left ( f \right ) b\sqrt{\pi }{\it Erf} \left ( \sqrt{-b\ln \left ( f \right ) }x \right ){\frac{1}{\sqrt{-b\ln \left ( f \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(b*x^2+a)/x^2,x)
[Out]
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Maxima [A] time = 0.82241, size = 38, normalized size = 0.78 \[ -\frac{\sqrt{-b x^{2} \log \left (f\right )} f^{a} \Gamma \left (-\frac{1}{2}, -b x^{2} \log \left (f\right )\right )}{2 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)/x^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.257619, size = 69, normalized size = 1.41 \[ \frac{\sqrt{\pi } b f^{a} x \operatorname{erf}\left (\sqrt{-b \log \left (f\right )} x\right ) \log \left (f\right ) - \sqrt{-b \log \left (f\right )} f^{b x^{2} + a}}{\sqrt{-b \log \left (f\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)/x^2,x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + b x^{2}}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(b*x**2+a)/x**2,x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{b x^{2} + a}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^2 + a)/x^2,x, algorithm="giac")
[Out]