Optimal. Leaf size=19 \[ \frac{2 \sinh ^{-1}\left (\frac{1}{2} \sqrt{b x+2}\right )}{b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0237856, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ \frac{2 \sinh ^{-1}\left (\frac{1}{2} \sqrt{b x+2}\right )}{b} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[2 + b*x]*Sqrt[6 + b*x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 4.56024, size = 14, normalized size = 0.74 \[ \frac{2 \operatorname{asinh}{\left (\frac{\sqrt{b x + 2}}{2} \right )}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b*x+2)**(1/2)/(b*x+6)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0121331, size = 19, normalized size = 1. \[ \frac{2 \sinh ^{-1}\left (\frac{1}{2} \sqrt{b x+2}\right )}{b} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[2 + b*x]*Sqrt[6 + b*x]),x]
[Out]
_______________________________________________________________________________________
Maple [B] time = 0.013, size = 66, normalized size = 3.5 \[{1\sqrt{ \left ( bx+2 \right ) \left ( bx+6 \right ) }\ln \left ({({b}^{2}x+4\,b){\frac{1}{\sqrt{{b}^{2}}}}}+\sqrt{{b}^{2}{x}^{2}+8\,bx+12} \right ){\frac{1}{\sqrt{bx+2}}}{\frac{1}{\sqrt{bx+6}}}{\frac{1}{\sqrt{{b}^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b*x+2)^(1/2)/(b*x+6)^(1/2),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(1/(sqrt(b*x + 6)*sqrt(b*x + 2)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.23159, size = 36, normalized size = 1.89 \[ -\frac{\log \left (-b x + \sqrt{b x + 6} \sqrt{b x + 2} - 4\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 6)*sqrt(b*x + 2)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{b x + 2} \sqrt{b x + 6}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b*x+2)**(1/2)/(b*x+6)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.267314, size = 32, normalized size = 1.68 \[ -\frac{2 \,{\rm ln}\left ({\left | -\sqrt{b x + 6} + \sqrt{b x + 2} \right |}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(b*x + 6)*sqrt(b*x + 2)),x, algorithm="giac")
[Out]