Optimal. Leaf size=29 \[ -\frac{2 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{\sqrt{33}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0459777, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.036 \[ -\frac{2 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{\sqrt{33}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 5.35424, size = 29, normalized size = 1. \[ - \frac{2 \sqrt{33} F\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{33} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**(1/2)/(2+3*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [C] time = 0.177449, size = 74, normalized size = 2.55 \[ \frac{i \sqrt{3 x+2} \sqrt{\frac{4 x-2}{5 x+3}} F\left (i \sinh ^{-1}\left (\frac{1}{\sqrt{15 x+9}}\right )|-\frac{33}{2}\right )}{\sqrt{1-2 x} \sqrt{\frac{3 x+2}{5 x+3}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - 2*x]*Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]
[Out]
_______________________________________________________________________________________
Maple [C] time = 0.02, size = 33, normalized size = 1.1 \[{\it EllipticF} \left ({\frac{\sqrt{11}\sqrt{2}}{11}\sqrt{3+5\,x}},{\frac{i}{2}}\sqrt{11}\sqrt{3}\sqrt{2} \right ) \sqrt{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^(1/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- 2 x + 1} \sqrt{3 x + 2} \sqrt{5 x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**(1/2)/(2+3*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*sqrt(3*x + 2)*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]