Optimal. Leaf size=43 \[ \frac{\sqrt{\pi } f^a \text{Erfi}\left (\sqrt{b} \sqrt{\log (f)} x^{n/2}\right )}{\sqrt{b} n \sqrt{\log (f)}} \]
[Out]
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Rubi [A] time = 0.0639646, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{\sqrt{\pi } f^a \text{Erfi}\left (\sqrt{b} \sqrt{\log (f)} x^{n/2}\right )}{\sqrt{b} n \sqrt{\log (f)}} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^n)*x^(-1 + n/2),x]
[Out]
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Rubi in Sympy [A] time = 5.5116, size = 39, normalized size = 0.91 \[ \frac{\sqrt{\pi } f^{a} \operatorname{erfi}{\left (\sqrt{b} x^{\frac{n}{2}} \sqrt{\log{\left (f \right )}} \right )}}{\sqrt{b} n \sqrt{\log{\left (f \right )}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b*x**n)*x**(-1+1/2*n),x)
[Out]
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Mathematica [A] time = 0.0332997, size = 46, normalized size = 1.07 \[ \frac{\sqrt{\pi } f^a x^{n/2} \left (\text{Erf}\left (\sqrt{-b \log (f) x^n}\right )-1\right )}{n \sqrt{-b \log (f) x^n}} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^n)*x^(-1 + n/2),x]
[Out]
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Maple [A] time = 0.068, size = 32, normalized size = 0.7 \[{\frac{{f}^{a}\sqrt{\pi }}{n}{\it Erf} \left ( \sqrt{-b\ln \left ( f \right ) }{x}^{{\frac{n}{2}}} \right ){\frac{1}{\sqrt{-b\ln \left ( f \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b*x^n)*x^(-1+1/2*n),x)
[Out]
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Maxima [A] time = 1.04757, size = 51, normalized size = 1.19 \[ \frac{\sqrt{\pi } f^{a} x^{\frac{1}{2} \, n}{\left (\operatorname{erf}\left (\sqrt{-b x^{n} \log \left (f\right )}\right ) - 1\right )}}{\sqrt{-b x^{n} \log \left (f\right )} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)*x^(1/2*n - 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.281294, size = 46, normalized size = 1.07 \[ \frac{\sqrt{\pi } f^{a} \operatorname{erf}\left (\sqrt{-b \log \left (f\right )} x x^{\frac{1}{2} \, n - 1}\right )}{\sqrt{-b \log \left (f\right )} n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)*x^(1/2*n - 1),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b*x**n)*x**(-1+1/2*n),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{b x^{n} + a} x^{\frac{1}{2} \, n - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)*x^(1/2*n - 1),x, algorithm="giac")
[Out]