Optimal. Leaf size=38 \[ \frac{\sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )}{\sqrt{b} \sqrt{\log (F)}} \]
[Out]
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Rubi [A] time = 0.0436502, antiderivative size = 38, 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 \[ \frac{\sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )}{\sqrt{b} \sqrt{\log (F)}} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*x)/Sqrt[x],x]
[Out]
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Rubi in Sympy [A] time = 5.11173, size = 37, normalized size = 0.97 \[ \frac{\sqrt{\pi } F^{a} \operatorname{erfi}{\left (\sqrt{b} \sqrt{x} \sqrt{\log{\left (F \right )}} \right )}}{\sqrt{b} \sqrt{\log{\left (F \right )}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(b*x+a)/x**(1/2),x)
[Out]
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Mathematica [A] time = 0.00747896, size = 38, normalized size = 1. \[ \frac{\sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )}{\sqrt{b} \sqrt{\log (F)}} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*x)/Sqrt[x],x]
[Out]
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Maple [A] time = 0.019, size = 27, normalized size = 0.7 \[{{F}^{a}\sqrt{\pi }{\it erfi} \left ( \sqrt{b}\sqrt{x}\sqrt{\ln \left ( F \right ) } \right ){\frac{1}{\sqrt{b}}}{\frac{1}{\sqrt{\ln \left ( F \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(b*x+a)/x^(1/2),x)
[Out]
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Maxima [A] time = 0.796128, size = 35, normalized size = 0.92 \[ \frac{\sqrt{\pi } F^{a} \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} \sqrt{x}\right )}{\sqrt{-b \log \left (F\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/sqrt(x),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.269375, size = 35, normalized size = 0.92 \[ \frac{\sqrt{\pi } F^{a} \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} \sqrt{x}\right )}{\sqrt{-b \log \left (F\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/sqrt(x),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + b x}}{\sqrt{x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(b*x+a)/x**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.257126, size = 41, normalized size = 1.08 \[ -\frac{\sqrt{\pi } \operatorname{erf}\left (-\sqrt{-b{\rm ln}\left (F\right )} \sqrt{x}\right ) e^{\left (a{\rm ln}\left (F\right )\right )}}{\sqrt{-b{\rm ln}\left (F\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/sqrt(x),x, algorithm="giac")
[Out]