Optimal. Leaf size=44 \[ \frac{f^{a+\frac{b}{x^3}}}{3 b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^3 \log (f)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0740412, antiderivative size = 44, 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 \[ \frac{f^{a+\frac{b}{x^3}}}{3 b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^3 \log (f)} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x^3)/x^7,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.56877, size = 36, normalized size = 0.82 \[ - \frac{f^{a + \frac{b}{x^{3}}}}{3 b x^{3} \log{\left (f \right )}} + \frac{f^{a + \frac{b}{x^{3}}}}{3 b^{2} \log{\left (f \right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x**3)/x**7,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0119088, size = 32, normalized size = 0.73 \[ \frac{f^{a+\frac{b}{x^3}} \left (x^3-b \log (f)\right )}{3 b^2 x^3 \log ^2(f)} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x^3)/x^7,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.022, size = 52, normalized size = 1.2 \[{\frac{1}{{x}^{6}} \left ({\frac{{x}^{6}}{3\, \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}}-{\frac{{x}^{3}}{3\,b\ln \left ( f \right ) }{{\rm e}^{ \left ( a+{\frac{b}{{x}^{3}}} \right ) \ln \left ( f \right ) }}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x^3)/x^7,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.811451, size = 30, normalized size = 0.68 \[ \frac{f^{a} \Gamma \left (2, -\frac{b \log \left (f\right )}{x^{3}}\right )}{3 \, b^{2} \log \left (f\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^7,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.251145, size = 46, normalized size = 1.05 \[ \frac{{\left (x^{3} - b \log \left (f\right )\right )} f^{\frac{a x^{3} + b}{x^{3}}}}{3 \, b^{2} x^{3} \log \left (f\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^7,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.250112, size = 29, normalized size = 0.66 \[ \frac{f^{a + \frac{b}{x^{3}}} \left (- b \log{\left (f \right )} + x^{3}\right )}{3 b^{2} x^{3} \log{\left (f \right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x**3)/x**7,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + \frac{b}{x^{3}}}}{x^{7}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x^3)/x^7,x, algorithm="giac")
[Out]