Optimal. Leaf size=41 \[ f^{\frac{c}{a}} \text{ExpIntegralEi}\left (-\frac{b c x \log (f)}{a (a+b x)}\right )-\text{ExpIntegralEi}\left (\frac{c \log (f)}{a+b x}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.204414, antiderivative size = 41, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.267 \[ f^{\frac{c}{a}} \text{ExpIntegralEi}\left (-\frac{b c x \log (f)}{a (a+b x)}\right )-\text{ExpIntegralEi}\left (\frac{c \log (f)}{a+b x}\right ) \]
Antiderivative was successfully verified.
[In] Int[f^(c/(a + b*x))/x,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 18.5461, size = 34, normalized size = 0.83 \[ f^{\frac{c}{a}} \operatorname{Ei}{\left (- \frac{b c x \log{\left (f \right )}}{a \left (a + b x\right )} \right )} - \operatorname{Ei}{\left (\frac{c \log{\left (f \right )}}{a + b x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(c/(b*x+a))/x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0188304, size = 41, normalized size = 1. \[ f^{\frac{c}{a}} \text{ExpIntegralEi}\left (-\frac{b c x \log (f)}{a^2+a b x}\right )-\text{ExpIntegralEi}\left (\frac{c \log (f)}{a+b x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[f^(c/(a + b*x))/x,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.027, size = 47, normalized size = 1.2 \[ -{f}^{{\frac{c}{a}}}{\it Ei} \left ( 1,-{\frac{c\ln \left ( f \right ) }{bx+a}}+{\frac{c\ln \left ( f \right ) }{a}} \right ) +{\it Ei} \left ( 1,-{\frac{c\ln \left ( f \right ) }{bx+a}} \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(c/(b*x+a))/x,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{b x + a}}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c/(b*x + a))/x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.261513, size = 55, normalized size = 1.34 \[ f^{\frac{c}{a}}{\rm Ei}\left (-\frac{b c x \log \left (f\right )}{a b x + a^{2}}\right ) -{\rm Ei}\left (\frac{c \log \left (f\right )}{b x + a}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c/(b*x + a))/x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{a + b x}}}{x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f**(c/(b*x+a))/x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{f^{\frac{c}{b x + a}}}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(c/(b*x + a))/x,x, algorithm="giac")
[Out]