Optimal. Leaf size=123 \[ \frac{16}{105} \sqrt{\pi } b^{7/2} F^a \log ^{\frac{7}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{16 b^3 \log ^3(F) F^{a+b x}}{105 \sqrt{x}}-\frac{8 b^2 \log ^2(F) F^{a+b x}}{105 x^{3/2}}-\frac{2 F^{a+b x}}{7 x^{7/2}}-\frac{4 b \log (F) F^{a+b x}}{35 x^{5/2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.175157, antiderivative size = 123, 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 \[ \frac{16}{105} \sqrt{\pi } b^{7/2} F^a \log ^{\frac{7}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )-\frac{16 b^3 \log ^3(F) F^{a+b x}}{105 \sqrt{x}}-\frac{8 b^2 \log ^2(F) F^{a+b x}}{105 x^{3/2}}-\frac{2 F^{a+b x}}{7 x^{7/2}}-\frac{4 b \log (F) F^{a+b x}}{35 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b*x)/x^(9/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 20.7114, size = 124, normalized size = 1.01 \[ \frac{16 \sqrt{\pi } F^{a} b^{\frac{7}{2}} \log{\left (F \right )}^{\frac{7}{2}} \operatorname{erfi}{\left (\sqrt{b} \sqrt{x} \sqrt{\log{\left (F \right )}} \right )}}{105} - \frac{16 F^{a + b x} b^{3} \log{\left (F \right )}^{3}}{105 \sqrt{x}} - \frac{8 F^{a + b x} b^{2} \log{\left (F \right )}^{2}}{105 x^{\frac{3}{2}}} - \frac{4 F^{a + b x} b \log{\left (F \right )}}{35 x^{\frac{5}{2}}} - \frac{2 F^{a + b x}}{7 x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(b*x+a)/x**(9/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.053314, size = 92, normalized size = 0.75 \[ -\frac{2 F^a \left (F^{b x} \left (8 b^3 x^3 \log ^3(F)+4 b^2 x^2 \log ^2(F)+6 b x \log (F)+15\right )-8 \sqrt{\pi } b^{7/2} x^{7/2} \log ^{\frac{7}{2}}(F) \text{Erfi}\left (\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right )\right )}{105 x^{7/2}} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b*x)/x^(9/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.02, size = 96, normalized size = 0.8 \[ -{\frac{{F}^{a}}{b} \left ( -b \right ) ^{{\frac{9}{2}}} \left ( \ln \left ( F \right ) \right ) ^{{\frac{7}{2}}} \left ( -{\frac{2\,{{\rm e}^{b\ln \left ( F \right ) x}}}{7} \left ({\frac{8\,{b}^{3}{x}^{3} \left ( \ln \left ( F \right ) \right ) ^{3}}{15}}+{\frac{4\,{b}^{2}{x}^{2} \left ( \ln \left ( F \right ) \right ) ^{2}}{15}}+{\frac{2\,b\ln \left ( F \right ) x}{5}}+1 \right ){x}^{-{\frac{7}{2}}} \left ( -b \right ) ^{-{\frac{7}{2}}} \left ( \ln \left ( F \right ) \right ) ^{-{\frac{7}{2}}}}+{\frac{16\,\sqrt{\pi }}{105}{b}^{{\frac{7}{2}}}{\it erfi} \left ( \sqrt{b}\sqrt{x}\sqrt{\ln \left ( F \right ) } \right ) \left ( -b \right ) ^{-{\frac{7}{2}}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(b*x+a)/x^(9/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.837909, size = 32, normalized size = 0.26 \[ -\frac{\left (-b x \log \left (F\right )\right )^{\frac{7}{2}} F^{a} \Gamma \left (-\frac{7}{2}, -b x \log \left (F\right )\right )}{x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(9/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.269327, size = 123, normalized size = 1. \[ \frac{2 \,{\left (8 \, \sqrt{\pi } F^{a} b^{4} x^{\frac{7}{2}} \operatorname{erf}\left (\sqrt{-b \log \left (F\right )} \sqrt{x}\right ) \log \left (F\right )^{4} -{\left (8 \, b^{3} x^{3} \log \left (F\right )^{3} + 4 \, b^{2} x^{2} \log \left (F\right )^{2} + 6 \, b x \log \left (F\right ) + 15\right )} \sqrt{-b \log \left (F\right )} F^{b x + a}\right )}}{105 \, \sqrt{-b \log \left (F\right )} x^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(9/2),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**(9/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{b x + a}}{x^{\frac{9}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(b*x + a)/x^(9/2),x, algorithm="giac")
[Out]