Optimal. Leaf size=71 \[ \frac{F^{a-\frac{b f}{d e-c f}} \text{ExpIntegralEi}\left (\frac{b d \log (F) (e+f x)}{(c+d x) (d e-c f)}\right )}{f}-\frac{F^a \text{ExpIntegralEi}\left (\frac{b \log (F)}{c+d x}\right )}{f} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.620657, antiderivative size = 71, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.19 \[ \frac{F^{a-\frac{b f}{d e-c f}} \text{ExpIntegralEi}\left (\frac{b d \log (F) (e+f x)}{(c+d x) (d e-c f)}\right )}{f}-\frac{F^a \text{ExpIntegralEi}\left (\frac{b \log (F)}{c+d x}\right )}{f} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x))/(e + f*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 27.4203, size = 65, normalized size = 0.92 \[ - \frac{F^{a} \operatorname{Ei}{\left (\frac{b \log{\left (F \right )}}{c + d x} \right )}}{f} + \frac{F^{\frac{a \left (c f - d e\right ) + b f}{c f - d e}} \operatorname{Ei}{\left (- \frac{b d \left (e + f x\right ) \log{\left (F \right )}}{\left (c + d x\right ) \left (c f - d e\right )} \right )}}{f} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c))/(f*x+e),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0864028, size = 66, normalized size = 0.93 \[ \frac{F^a \left (F^{\frac{b f}{c f-d e}} \text{ExpIntegralEi}\left (\frac{b d \log (F) (e+f x)}{(c+d x) (d e-c f)}\right )-\text{ExpIntegralEi}\left (\frac{b \log (F)}{c+d x}\right )\right )}{f} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x))/(e + f*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.043, size = 106, normalized size = 1.5 \[ -{\frac{1}{f}{F}^{{\frac{acf-ade+bf}{cf-ed}}}{\it Ei} \left ( 1,-{\frac{b\ln \left ( F \right ) }{dx+c}}-\ln \left ( F \right ) a-{\frac{-\ln \left ( F \right ) acf+\ln \left ( F \right ) ade-\ln \left ( F \right ) bf}{cf-ed}} \right ) }+{\frac{{F}^{a}}{f}{\it Ei} \left ( 1,-{\frac{b\ln \left ( F \right ) }{dx+c}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c))/(f*x+e),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{d x + c}}}{f x + e}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c))/(f*x + e),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.282594, size = 120, normalized size = 1.69 \[ \frac{F^{\frac{a d e -{\left (a c + b\right )} f}{d e - c f}}{\rm Ei}\left (\frac{{\left (b d f x + b d e\right )} \log \left (F\right )}{c d e - c^{2} f +{\left (d^{2} e - c d f\right )} x}\right ) - F^{a}{\rm Ei}\left (\frac{b \log \left (F\right )}{d x + c}\right )}{f} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c))/(f*x + e),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/(d*x+c))/(f*x+e),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{d x + c}}}{f x + e}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c))/(f*x + e),x, algorithm="giac")
[Out]