Optimal. Leaf size=62 \[ \frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{11 \sqrt{1-2 x}}+\sqrt{\frac{3}{11}} E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right ) \]
[Out]
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Rubi [A] time = 0.0885502, antiderivative size = 62, 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 \[ \frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{11 \sqrt{1-2 x}}+\sqrt{\frac{3}{11}} E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right ) \]
Antiderivative was successfully verified.
[In] Int[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
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Rubi in Sympy [A] time = 9.10118, size = 54, normalized size = 0.87 \[ \frac{\sqrt{33} E\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{11} + \frac{2 \sqrt{3 x + 2} \sqrt{5 x + 3}}{11 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**(1/2)/(1-2*x)**(3/2)/(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0864648, size = 91, normalized size = 1.47 \[ \frac{1}{11} \left (\frac{2 \sqrt{3 x+2} \sqrt{5 x+3}}{\sqrt{1-2 x}}+\sqrt{2} F\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )-\sqrt{2} E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )\right ) \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[2 + 3*x]/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
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Maple [C] time = 0.026, size = 158, normalized size = 2.6 \[ -{\frac{1}{330\,{x}^{3}+253\,{x}^{2}-77\,x-66}\sqrt{1-2\,x}\sqrt{2+3\,x}\sqrt{3+5\,x} \left ( \sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticF} \left ({\frac{\sqrt{11}\sqrt{2}}{11}\sqrt{3+5\,x}},{\frac{i}{2}}\sqrt{11}\sqrt{3}\sqrt{2} \right ) -\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ({\frac{\sqrt{11}\sqrt{2}}{11}\sqrt{3+5\,x}},{\frac{i}{2}}\sqrt{11}\sqrt{3}\sqrt{2} \right ) +30\,{x}^{2}+38\,x+12 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^(1/2)/(1-2*x)^(3/2)/(3+5*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{3 \, x + 2}}{\sqrt{5 \, x + 3}{\left (-2 \, x + 1\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x + 2)/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (-\frac{\sqrt{3 \, x + 2}}{\sqrt{5 \, x + 3}{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x + 2)/(sqrt(5*x + 3)*(-2*x + 1)^(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((2+3*x)**(1/2)/(1-2*x)**(3/2)/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{3 \, x + 2}}{\sqrt{5 \, x + 3}{\left (-2 \, x + 1\right )}^{\frac{3}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(3*x + 2)/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]