Optimal. Leaf size=22 \[ -\frac{F^a \text{ExpIntegralEi}\left (\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0713568, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ -\frac{F^a \text{ExpIntegralEi}\left (\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x)^2)/(c + d*x),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.86458, size = 20, normalized size = 0.91 \[ - \frac{F^{a} \operatorname{Ei}{\left (\frac{b \log{\left (F \right )}}{\left (c + d x\right )^{2}} \right )}}{2 d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c)**2)/(d*x+c),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00934062, size = 22, normalized size = 1. \[ -\frac{F^a \text{ExpIntegralEi}\left (\frac{b \log (F)}{(c+d x)^2}\right )}{2 d} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x)^2)/(c + d*x),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.029, size = 23, normalized size = 1.1 \[{\frac{{F}^{a}}{2\,d}{\it Ei} \left ( 1,-{\frac{b\ln \left ( F \right ) }{ \left ( dx+c \right ) ^{2}}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c)^2)/(d*x+c),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{{\left (d x + c\right )}^{2}}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^2)/(d*x + c),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.26512, size = 42, normalized size = 1.91 \[ -\frac{F^{a}{\rm Ei}\left (\frac{b \log \left (F\right )}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right )}{2 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^2)/(d*x + c),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{\left (c + d x\right )^{2}}}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b/(d*x+c)**2)/(d*x+c),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{a + \frac{b}{{\left (d x + c\right )}^{2}}}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c)^2)/(d*x + c),x, algorithm="giac")
[Out]