Optimal. Leaf size=20 \[ \frac{\log \left (\sqrt{-a} x+a\right )}{\sqrt{-a}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0179456, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ \frac{\log \left (\sqrt{-a} x+a\right )}{\sqrt{-a}} \]
Antiderivative was successfully verified.
[In] Int[(a + Sqrt[-a]*x)^(-1),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.67653, size = 17, normalized size = 0.85 \[ \frac{\log{\left (a + x \sqrt{- a} \right )}}{\sqrt{- a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+x*(-a)**(1/2)),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00722106, size = 20, normalized size = 1. \[ \frac{\log \left (\sqrt{-a} x+a\right )}{\sqrt{-a}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + Sqrt[-a]*x)^(-1),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.002, size = 17, normalized size = 0.9 \[{1\ln \left ( a+x\sqrt{-a} \right ){\frac{1}{\sqrt{-a}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+x*(-a)^(1/2)),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34102, size = 22, normalized size = 1.1 \[ \frac{\log \left (\sqrt{-a} x + a\right )}{\sqrt{-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-a)*x + a),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.218946, size = 22, normalized size = 1.1 \[ \frac{\log \left (\sqrt{-a} x + a\right )}{\sqrt{-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-a)*x + a),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.089785, size = 17, normalized size = 0.85 \[ \frac{\log{\left (a + x \sqrt{- a} \right )}}{\sqrt{- a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+x*(-a)**(1/2)),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.203512, size = 23, normalized size = 1.15 \[ \frac{{\rm ln}\left ({\left | \sqrt{-a} x + a \right |}\right )}{\sqrt{-a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(-a)*x + a),x, algorithm="giac")
[Out]