Optimal. Leaf size=38 \[ \frac{b f^a \log (f) \text{ExpIntegralEi}\left (b \log (f) x^n\right )}{n}-\frac{x^{-n} f^{a+b x^n}}{n} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0772465, antiderivative size = 38, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118 \[ \frac{b f^a \log (f) \text{ExpIntegralEi}\left (b \log (f) x^n\right )}{n}-\frac{x^{-n} f^{a+b x^n}}{n} \]
Antiderivative was successfully verified.
[In] Int[f^(a + b*x^n)*x^(-1 - n),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.79894, size = 32, normalized size = 0.84 \[ \frac{b f^{a} \log{\left (f \right )} \operatorname{Ei}{\left (b x^{n} \log{\left (f \right )} \right )}}{n} - \frac{f^{a + b x^{n}} x^{- n}}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(f**(a+b*x**n)*x**(-1-n),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0195919, size = 38, normalized size = 1. \[ \frac{b f^a \log (f) \text{ExpIntegralEi}\left (b \log (f) x^n\right )}{n}-\frac{x^{-n} f^{a+b x^n}}{n} \]
Antiderivative was successfully verified.
[In] Integrate[f^(a + b*x^n)*x^(-1 - n),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.05, size = 42, normalized size = 1.1 \[ -{\frac{{f}^{a+b{x}^{n}}}{n{x}^{n}}}-{\frac{b\ln \left ( f \right ){f}^{a}{\it Ei} \left ( 1,-b{x}^{n}\ln \left ( f \right ) \right ) }{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(f^(a+b*x^n)*x^(-1-n),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.07261, size = 27, normalized size = 0.71 \[ \frac{b f^{a} \Gamma \left (-1, -b x^{n} \log \left (f\right )\right ) \log \left (f\right )}{n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)*x^(-n - 1),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.256526, size = 58, normalized size = 1.53 \[ \frac{b f^{a} x^{n}{\rm Ei}\left (b x^{n} \log \left (f\right )\right ) \log \left (f\right ) - e^{\left (b x^{n} \log \left (f\right ) + a \log \left (f\right )\right )}}{n x^{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)*x^(-n - 1),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**n)*x**(-1-n),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int f^{b x^{n} + a} x^{-n - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(f^(b*x^n + a)*x^(-n - 1),x, algorithm="giac")
[Out]