Optimal. Leaf size=131 \[ \frac{105 \sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )}{16 b^{9/2} \log ^{\frac{9}{2}}(F)}-\frac{105 \sqrt{x} F^{a+b x}}{8 b^4 \log ^4(F)}+\frac{35 x^{3/2} F^{a+b x}}{4 b^3 \log ^3(F)}-\frac{7 x^{5/2} F^{a+b x}}{2 b^2 \log ^2(F)}+\frac{x^{7/2} F^{a+b x}}{b \log (F)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.242796, antiderivative size = 131, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{105 \sqrt{\pi } F^a \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )}{16 b^{9/2} \log ^{\frac{9}{2}}(F)}-\frac{105 \sqrt{x} F^{a+b x}}{8 b^4 \log ^4(F)}+\frac{35 x^{3/2} F^{a+b x}}{4 b^3 \log ^3(F)}-\frac{7 x^{5/2} F^{a+b x}}{2 b^2 \log ^2(F)}+\frac{x^{7/2} F^{a+b x}}{b \log (F)} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*x)*x^(7/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 26.9223, size = 129, normalized size = 0.98 \[ \frac{105 \sqrt{\pi } F^{a} \operatorname{erfi}{\left (\sqrt{b} \sqrt{x} \sqrt{\log{\left (F \right )}} \right )}}{16 b^{\frac{9}{2}} \log{\left (F \right )}^{\frac{9}{2}}} + \frac{F^{a + b x} x^{\frac{7}{2}}}{b \log{\left (F \right )}} - \frac{7 F^{a + b x} x^{\frac{5}{2}}}{2 b^{2} \log{\left (F \right )}^{2}} + \frac{35 F^{a + b x} x^{\frac{3}{2}}}{4 b^{3} \log{\left (F \right )}^{3}} - \frac{105 F^{a + b x} \sqrt{x}}{8 b^{4} \log{\left (F \right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(b*x+a)*x**(7/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0971548, size = 99, normalized size = 0.76 \[ \frac{F^a \left (2 \sqrt{b} \sqrt{x} \sqrt{\log (F)} F^{b x} \left (8 b^3 x^3 \log ^3(F)-28 b^2 x^2 \log ^2(F)+70 b x \log (F)-105\right )+105 \sqrt{\pi } \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )\right )}{16 b^{9/2} \log ^{\frac{9}{2}}(F)} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*x)*x^(7/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.158, size = 99, normalized size = 0.8 \[ -{\frac{{F}^{a}}{b} \left ( -{\frac{ \left ( -72\,{b}^{3}{x}^{3} \left ( \ln \left ( F \right ) \right ) ^{3}+252\,{b}^{2}{x}^{2} \left ( \ln \left ( F \right ) \right ) ^{2}-630\,b\ln \left ( F \right ) x+945 \right ){{\rm e}^{b\ln \left ( F \right ) x}}}{72\,{b}^{4}}\sqrt{x} \left ( -b \right ) ^{{\frac{9}{2}}}\sqrt{\ln \left ( F \right ) }}+{\frac{105\,\sqrt{\pi }}{16} \left ( -b \right ) ^{{\frac{9}{2}}}{\it erfi} \left ( \sqrt{b}\sqrt{x}\sqrt{\ln \left ( F \right ) } \right ){b}^{-{\frac{9}{2}}}} \right ) \left ( -b \right ) ^{-{\frac{7}{2}}} \left ( \ln \left ( F \right ) \right ) ^{-{\frac{9}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(b*x+a)*x^(7/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.819579, size = 120, normalized size = 0.92 \[ \frac{1}{16} \, F^{a}{\left (\frac{2 \,{\left (8 \, b^{3} x^{\frac{7}{2}} \log \left (F\right )^{3} - 28 \, b^{2} x^{\frac{5}{2}} \log \left (F\right )^{2} + 70 \, b x^{\frac{3}{2}} \log \left (F\right ) - 105 \, \sqrt{x}\right )} F^{b x}}{b^{4} \log \left (F\right )^{4}} + \frac{105 \, \sqrt{\pi } \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} \sqrt{x}\right )}{\sqrt{-b \log \left (F\right )} b^{4} \log \left (F\right )^{4}}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)*x^(7/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.274976, size = 119, normalized size = 0.91 \[ \frac{2 \,{\left (8 \, b^{3} x^{3} \log \left (F\right )^{3} - 28 \, b^{2} x^{2} \log \left (F\right )^{2} + 70 \, b x \log \left (F\right ) - 105\right )} \sqrt{-b \log \left (F\right )} F^{b x + a} \sqrt{x} + 105 \, \sqrt{\pi } F^{a} \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} \sqrt{x}\right )}{16 \, \sqrt{-b \log \left (F\right )} b^{4} \log \left (F\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)*x^(7/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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**(7/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.257172, size = 130, normalized size = 0.99 \[ \frac{{\left (8 \, b^{3} x^{\frac{7}{2}}{\rm ln}\left (F\right )^{3} - 28 \, b^{2} x^{\frac{5}{2}}{\rm ln}\left (F\right )^{2} + 70 \, b x^{\frac{3}{2}}{\rm ln}\left (F\right ) - 105 \, \sqrt{x}\right )} e^{\left (b x{\rm ln}\left (F\right ) + a{\rm ln}\left (F\right )\right )}}{8 \, b^{4}{\rm ln}\left (F\right )^{4}} - \frac{105 \, \sqrt{\pi } \operatorname{erf}\left (-\sqrt{-b{\rm ln}\left (F\right )} \sqrt{x}\right ) e^{\left (a{\rm ln}\left (F\right )\right )}}{16 \, \sqrt{-b{\rm ln}\left (F\right )} b^{4}{\rm ln}\left (F\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)*x^(7/2),x, algorithm="giac")
[Out]