Optimal. Leaf size=77 \[ \frac{4}{3} \sqrt{\pi } b^{3/2} F^a \log ^{\frac{3}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{2 F^{a+b x}}{3 x^{3/2}}-\frac{4 b \log (F) F^{a+b x}}{3 \sqrt{x}} \]
[Out]
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Rubi [A] time = 0.106497, antiderivative size = 77, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{4}{3} \sqrt{\pi } b^{3/2} F^a \log ^{\frac{3}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{2 F^{a+b x}}{3 x^{3/2}}-\frac{4 b \log (F) F^{a+b x}}{3 \sqrt{x}} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*x)/x^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 11.7905, size = 76, normalized size = 0.99 \[ \frac{4 \sqrt{\pi } F^{a} b^{\frac{3}{2}} \log{\left (F \right )}^{\frac{3}{2}} \operatorname{erfi}{\left (\sqrt{b} \sqrt{x} \sqrt{\log{\left (F \right )}} \right )}}{3} - \frac{4 F^{a + b x} b \log{\left (F \right )}}{3 \sqrt{x}} - \frac{2 F^{a + b x}}{3 x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(b*x+a)/x**(5/2),x)
[Out]
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Mathematica [A] time = 0.0651847, size = 64, normalized size = 0.83 \[ \frac{2}{3} F^a \left (2 \sqrt{\pi } b^{3/2} \log ^{\frac{3}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{F^{b x} (2 b x \log (F)+1)}{x^{3/2}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*x)/x^(5/2),x]
[Out]
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Maple [A] time = 0.019, size = 72, normalized size = 0.9 \[ -{\frac{{F}^{a}}{b} \left ( -b \right ) ^{{\frac{5}{2}}} \left ( \ln \left ( F \right ) \right ) ^{{\frac{3}{2}}} \left ( -{\frac{ \left ( 4\,b\ln \left ( F \right ) x+2 \right ){{\rm e}^{b\ln \left ( F \right ) x}}}{3}{x}^{-{\frac{3}{2}}} \left ( -b \right ) ^{-{\frac{3}{2}}} \left ( \ln \left ( F \right ) \right ) ^{-{\frac{3}{2}}}}+{\frac{4\,\sqrt{\pi }}{3}{b}^{{\frac{3}{2}}}{\it erfi} \left ( \sqrt{b}\sqrt{x}\sqrt{\ln \left ( F \right ) } \right ) \left ( -b \right ) ^{-{\frac{3}{2}}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(b*x+a)/x^(5/2),x)
[Out]
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Maxima [A] time = 0.836279, size = 32, normalized size = 0.42 \[ -\frac{\left (-b x \log \left (F\right )\right )^{\frac{3}{2}} F^{a} \Gamma \left (-\frac{3}{2}, -b x \log \left (F\right )\right )}{x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.276743, size = 90, normalized size = 1.17 \[ \frac{2 \,{\left (2 \, \sqrt{\pi } F^{a} b^{2} x^{\frac{3}{2}} \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} \sqrt{x}\right ) \log \left (F\right )^{2} -{\left (2 \, b x \log \left (F\right ) + 1\right )} \sqrt{-b \log \left (F\right )} F^{b x + a}\right )}}{3 \, \sqrt{-b \log \left (F\right )} x^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(5/2),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**(b*x+a)/x**(5/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{b x + a}}{x^{\frac{5}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(5/2),x, algorithm="giac")
[Out]