Optimal. Leaf size=35 \[ 2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left (\frac{\sqrt{a+b x}}{\sqrt{a}}\right ) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0346436, antiderivative size = 35, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ 2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left (\frac{\sqrt{a+b x}}{\sqrt{a}}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[a + b*x]/x,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.70595, size = 31, normalized size = 0.89 \[ - 2 \sqrt{a} \operatorname{atanh}{\left (\frac{\sqrt{a + b x}}{\sqrt{a}} \right )} + 2 \sqrt{a + b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(1/2)/x,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0171722, size = 35, normalized size = 1. \[ 2 \sqrt{a+b x}-2 \sqrt{a} \tanh ^{-1}\left (\frac{\sqrt{a+b x}}{\sqrt{a}}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[a + b*x]/x,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.022, size = 28, normalized size = 0.8 \[ -2\,{\it Artanh} \left ({\frac{\sqrt{bx+a}}{\sqrt{a}}} \right ) \sqrt{a}+2\,\sqrt{bx+a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(1/2)/x,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + a)/x,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.224733, size = 1, normalized size = 0.03 \[ \left [\sqrt{a} \log \left (\frac{b x - 2 \, \sqrt{b x + a} \sqrt{a} + 2 \, a}{x}\right ) + 2 \, \sqrt{b x + a}, -2 \, \sqrt{-a} \arctan \left (\frac{\sqrt{b x + a}}{\sqrt{-a}}\right ) + 2 \, \sqrt{b x + a}\right ] \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + a)/x,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 4.84184, size = 68, normalized size = 1.94 \[ - 2 \sqrt{a} \operatorname{asinh}{\left (\frac{\sqrt{a}}{\sqrt{b} \sqrt{x}} \right )} + \frac{2 a}{\sqrt{b} \sqrt{x} \sqrt{\frac{a}{b x} + 1}} + \frac{2 \sqrt{b} \sqrt{x}}{\sqrt{\frac{a}{b x} + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x+a)**(1/2)/x,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.205686, size = 43, normalized size = 1.23 \[ \frac{2 \, a \arctan \left (\frac{\sqrt{b x + a}}{\sqrt{-a}}\right )}{\sqrt{-a}} + 2 \, \sqrt{b x + a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x + a)/x,x, algorithm="giac")
[Out]