Optimal. Leaf size=39 \[ \frac{f^{a+\frac{b}{x}}}{b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x}}}{b x \log (f)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0625852, antiderivative size = 39, 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 \[ \frac{f^{a+\frac{b}{x}}}{b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x}}}{b x \log (f)} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b/x)/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 6.6541, size = 27, normalized size = 0.69 \[ - \frac{f^{a + \frac{b}{x}}}{b x \log{\left (f \right )}} + \frac{f^{a + \frac{b}{x}}}{b^{2} \log{\left (f \right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b/x)/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0107066, size = 27, normalized size = 0.69 \[ \frac{f^{a+\frac{b}{x}} (x-b \log (f))}{b^2 x \log ^2(f)} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b/x)/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 49, normalized size = 1.3 \[{\frac{1}{{x}^{2}} \left ({\frac{{x}^{2}}{ \left ( \ln \left ( f \right ) \right ) ^{2}{b}^{2}}{{\rm e}^{ \left ( a+{\frac{b}{x}} \right ) \ln \left ( f \right ) }}}-{\frac{x}{b\ln \left ( f \right ) }{{\rm e}^{ \left ( a+{\frac{b}{x}} \right ) \ln \left ( f \right ) }}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b/x)/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.821745, size = 28, normalized size = 0.72 \[ \frac{f^{a} \Gamma \left (2, -\frac{b \log \left (f\right )}{x}\right )}{b^{2} \log \left (f\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x)/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.260734, size = 42, normalized size = 1.08 \[ -\frac{{\left (b \log \left (f\right ) - x\right )} f^{\frac{a x + b}{x}}}{b^{2} x \log \left (f\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x)/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.248367, size = 22, normalized size = 0.56 \[ \frac{f^{a + \frac{b}{x}} \left (- b \log{\left (f \right )} + x\right )}{b^{2} x \log{\left (f \right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(a+b/x)/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{a + \frac{b}{x}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(a + b/x)/x^3,x, algorithm="giac")
[Out]