Optimal. Leaf size=119 \[ -\frac{8}{105} \sqrt{\pi } b^{7/2} f^a \log ^{\frac{7}{2}}(f) \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right )+\frac{8}{105} b^3 x \log ^3(f) f^{a+\frac{b}{x^2}}+\frac{4}{105} b^2 x^3 \log ^2(f) f^{a+\frac{b}{x^2}}+\frac{1}{7} x^7 f^{a+\frac{b}{x^2}}+\frac{2}{35} b x^5 \log (f) f^{a+\frac{b}{x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.193734, antiderivative size = 119, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.308 \[ -\frac{8}{105} \sqrt{\pi } b^{7/2} f^a \log ^{\frac{7}{2}}(f) \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right )+\frac{8}{105} b^3 x \log ^3(f) f^{a+\frac{b}{x^2}}+\frac{4}{105} b^2 x^3 \log ^2(f) f^{a+\frac{b}{x^2}}+\frac{1}{7} x^7 f^{a+\frac{b}{x^2}}+\frac{2}{35} b x^5 \log (f) f^{a+\frac{b}{x^2}} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x^2)*x^6,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 17.9099, size = 117, normalized size = 0.98 \[ - \frac{8 \sqrt{\pi } b^{\frac{7}{2}} f^{a} \log{\left (f \right )}^{\frac{7}{2}} \operatorname{erfi}{\left (\frac{\sqrt{b} \sqrt{\log{\left (f \right )}}}{x} \right )}}{105} + \frac{8 b^{3} f^{a + \frac{b}{x^{2}}} x \log{\left (f \right )}^{3}}{105} + \frac{4 b^{2} f^{a + \frac{b}{x^{2}}} x^{3} \log{\left (f \right )}^{2}}{105} + \frac{2 b f^{a + \frac{b}{x^{2}}} x^{5} \log{\left (f \right )}}{35} + \frac{f^{a + \frac{b}{x^{2}}} x^{7}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x**2)*x**6,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0510242, size = 86, normalized size = 0.72 \[ \frac{1}{105} f^a \left (x f^{\frac{b}{x^2}} \left (8 b^3 \log ^3(f)+4 b^2 x^2 \log ^2(f)+6 b x^4 \log (f)+15 x^6\right )-8 \sqrt{\pi } b^{7/2} \log ^{\frac{7}{2}}(f) \text{Erfi}\left (\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x^2)*x^6,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.036, size = 111, normalized size = 0.9 \[{\frac{{f}^{a}{x}^{7}}{7}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{2\,{f}^{a}\ln \left ( f \right ) b{x}^{5}}{35}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{4\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}{x}^{3}}{105}{f}^{{\frac{b}{{x}^{2}}}}}+{\frac{8\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{3}{b}^{3}x}{105}{f}^{{\frac{b}{{x}^{2}}}}}-{\frac{8\,{f}^{a} \left ( \ln \left ( f \right ) \right ) ^{4}{b}^{4}\sqrt{\pi }}{105}{\it Erf} \left ({\frac{1}{x}\sqrt{-b\ln \left ( f \right ) }} \right ){\frac{1}{\sqrt{-b\ln \left ( f \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x^2)*x^6,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.831959, size = 134, normalized size = 1.13 \[ -\frac{8 \, \sqrt{\pi } b^{4} f^{a}{\left (\operatorname{erf}\left (\sqrt{-\frac{b \log \left (f\right )}{x^{2}}}\right ) - 1\right )} \log \left (f\right )^{4}}{105 \, x \sqrt{-\frac{b \log \left (f\right )}{x^{2}}}} + \frac{1}{105} \,{\left (15 \, f^{a} x^{7} + 6 \, b f^{a} x^{5} \log \left (f\right ) + 4 \, b^{2} f^{a} x^{3} \log \left (f\right )^{2} + 8 \, b^{3} f^{a} x \log \left (f\right )^{3}\right )} f^{\frac{b}{x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)*x^6,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.265439, size = 128, normalized size = 1.08 \[ -\frac{8 \, \sqrt{\pi } b^{4} f^{a} \operatorname{erf}\left (\frac{\sqrt{-b \log \left (f\right )}}{x}\right ) \log \left (f\right )^{4} -{\left (15 \, x^{7} + 6 \, b x^{5} \log \left (f\right ) + 4 \, b^{2} x^{3} \log \left (f\right )^{2} + 8 \, b^{3} x \log \left (f\right )^{3}\right )} \sqrt{-b \log \left (f\right )} f^{\frac{a x^{2} + b}{x^{2}}}}{105 \, \sqrt{-b \log \left (f\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)*x^6,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**(a+b/x**2)*x**6,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{a + \frac{b}{x^{2}}} x^{6}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^2)*x^6,x, algorithm="giac")
[Out]