Optimal. Leaf size=61 \[ \frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{\sqrt{3 x+2}}-2 \sqrt{\frac{11}{3}} E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right ) \]
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Rubi [A] time = 0.0868808, 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 \[ \frac{2 \sqrt{1-2 x} \sqrt{5 x+3}}{\sqrt{3 x+2}}-2 \sqrt{\frac{11}{3}} E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
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Rubi in Sympy [A] time = 9.42041, size = 54, normalized size = 0.89 \[ \frac{2 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{\sqrt{3 x + 2}} - \frac{2 \sqrt{33} E\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(1/2)/(2+3*x)**(3/2)/(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.151324, size = 106, normalized size = 1.74 \[ \frac{6 \sqrt{1-2 x} \sqrt{3 x+2} \sqrt{5 x+3}-2 \sqrt{2} (3 x+2) F\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )+2 \sqrt{2} (3 x+2) E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )}{9 x+6} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
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Maple [C] time = 0.024, size = 158, normalized size = 2.6 \[{\frac{2}{90\,{x}^{3}+69\,{x}^{2}-21\,x-18}\sqrt{1-2\,x}\sqrt{2+3\,x}\sqrt{3+5\,x} \left ( \sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticF} \left ({\frac{\sqrt{11}\sqrt{2}}{11}\sqrt{3+5\,x}},{\frac{i}{2}}\sqrt{11}\sqrt{3}\sqrt{2} \right ) -\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ({\frac{\sqrt{11}\sqrt{2}}{11}\sqrt{3+5\,x}},{\frac{i}{2}}\sqrt{11}\sqrt{3}\sqrt{2} \right ) +30\,{x}^{2}+3\,x-9 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(1/2)/(2+3*x)^(3/2)/(3+5*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}{\left (3 \, x + 2\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/(sqrt(5*x + 3)*(3*x + 2)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}{\left (3 \, x + 2\right )}^{\frac{3}{2}}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/(sqrt(5*x + 3)*(3*x + 2)^(3/2)),x, algorithm="fricas")
[Out]
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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)/(2+3*x)**(3/2)/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3}{\left (3 \, x + 2\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/(sqrt(5*x + 3)*(3*x + 2)^(3/2)),x, algorithm="giac")
[Out]