Optimal. Leaf size=25 \[ -\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0659469, antiderivative size = 25, 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 \[ -\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)} \]
Antiderivative was successfully verified.
[In] Int[F^(a + b/(c + d*x))/(c + d*x)^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.35887, size = 17, normalized size = 0.68 \[ - \frac{F^{a + \frac{b}{c + d x}}}{b d \log{\left (F \right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(F**(a+b/(d*x+c))/(d*x+c)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0106558, size = 25, normalized size = 1. \[ -\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)} \]
Antiderivative was successfully verified.
[In] Integrate[F^(a + b/(c + d*x))/(c + d*x)^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 26, normalized size = 1. \[ -{\frac{1}{\ln \left ( F \right ) bd}{F}^{a+{\frac{b}{dx+c}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(F^(a+b/(d*x+c))/(d*x+c)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.775547, size = 34, normalized size = 1.36 \[ -\frac{F^{a + \frac{b}{d x + c}}}{b d \log \left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c))/(d*x + c)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.260342, size = 42, normalized size = 1.68 \[ -\frac{F^{\frac{a d x + a c + b}{d x + c}}}{b d \log \left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c))/(d*x + c)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.712625, size = 34, normalized size = 1.36 \[ \begin{cases} - \frac{F^{a + \frac{b}{c + d x}}}{b d \log{\left (F \right )}} & \text{for}\: b d \log{\left (F \right )} \neq 0 \\- \frac{1}{c d + d^{2} x} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F**(a+b/(d*x+c))/(d*x+c)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.254895, size = 34, normalized size = 1.36 \[ -\frac{F^{a + \frac{b}{d x + c}}}{b d{\rm ln}\left (F\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(F^(a + b/(d*x + c))/(d*x + c)^2,x, algorithm="giac")
[Out]