Optimal. Leaf size=61 \[ 2 \sqrt{\frac{7}{5}} E\left (\sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )|\frac{33}{35}\right )-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0876837, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.107 \[ 2 \sqrt{\frac{7}{5}} E\left (\sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )|\frac{33}{35}\right )-\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.61802, size = 54, normalized size = 0.89 \[ - \frac{2 \sqrt{- 2 x + 1} \sqrt{3 x + 2}}{\sqrt{5 x + 3}} + \frac{2 \sqrt{35} E\left (\operatorname{asin}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}\middle | \frac{33}{35}\right )}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(1/2)/(3+5*x)**(3/2)/(2+3*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.150551, size = 61, normalized size = 1. \[ -\frac{2 \sqrt{1-2 x} \sqrt{3 x+2}}{\sqrt{5 x+3}}-\frac{2}{5} \sqrt{2} E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)),x]
[Out]
_______________________________________________________________________________________
Maple [C] time = 0.024, size = 104, normalized size = 1.7 \[{\frac{2}{150\,{x}^{3}+115\,{x}^{2}-35\,x-30}\sqrt{1-2\,x}\sqrt{2+3\,x}\sqrt{3+5\,x} \left ( \sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ({\frac{\sqrt{11}\sqrt{2}}{11}\sqrt{3+5\,x}},{\frac{i}{2}}\sqrt{11}\sqrt{3}\sqrt{2} \right ) -30\,{x}^{2}-5\,x+10 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(1/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-2 \, x + 1}}{{\left (5 \, x + 3\right )}^{\frac{3}{2}} \sqrt{3 \, x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/((5*x + 3)^(3/2)*sqrt(3*x + 2)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{-2 \, x + 1}}{{\left (5 \, x + 3\right )}^{\frac{3}{2}} \sqrt{3 \, x + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/((5*x + 3)^(3/2)*sqrt(3*x + 2)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(1/2)/(3+5*x)**(3/2)/(2+3*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-2 \, x + 1}}{{\left (5 \, x + 3\right )}^{\frac{3}{2}} \sqrt{3 \, x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/((5*x + 3)^(3/2)*sqrt(3*x + 2)),x, algorithm="giac")
[Out]