Optimal. Leaf size=49 \[ \frac{2 \sqrt{\frac{7}{5}} \sqrt{-5 x-3} E\left (\sin ^{-1}\left (\sqrt{5} \sqrt{3 x+2}\right )|\frac{2}{35}\right )}{3 \sqrt{5 x+3}} \]
[Out]
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Rubi [A] time = 0.093612, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071 \[ \frac{2 \sqrt{\frac{7}{5}} \sqrt{-5 x-3} E\left (\sin ^{-1}\left (\sqrt{5} \sqrt{3 x+2}\right )|\frac{2}{35}\right )}{3 \sqrt{5 x+3}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]
[Out]
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Rubi in Sympy [A] time = 9.14623, size = 65, normalized size = 1.33 \[ \frac{2 \sqrt{5} \sqrt{- 15 x - 9} \sqrt{- 2 x + 1} E\left (\operatorname{asin}{\left (\sqrt{5} \sqrt{3 x + 2} \right )}\middle | \frac{2}{35}\right )}{15 \sqrt{- \frac{6 x}{7} + \frac{3}{7}} \sqrt{5 x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(1/2)/(2+3*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.372234, size = 121, normalized size = 2.47 \[ \frac{2 \sqrt{1-2 x} \left (5 \left (6 x^2+x-2\right ) \sqrt{5 x+3}+\sqrt{33} \sqrt{\frac{2 x-1}{5 x+3}} \sqrt{\frac{3 x+2}{5 x+3}} (5 x+3)^2 E\left (\sin ^{-1}\left (\frac{\sqrt{\frac{11}{2}}}{\sqrt{5 x+3}}\right )|-\frac{2}{33}\right )\right )}{15 \sqrt{3 x+2} \left (10 x^2+x-3\right )} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]/(Sqrt[2 + 3*x]*Sqrt[3 + 5*x]),x]
[Out]
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Maple [C] time = 0.018, size = 67, normalized size = 1.4 \[{\frac{\sqrt{2}}{15} \left ( 35\,{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) -2\,{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(1/2)/(2+3*x)^(1/2)/(3+5*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/(sqrt(5*x + 3)*sqrt(3*x + 2)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{\sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/(sqrt(5*x + 3)*sqrt(3*x + 2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{- 2 x + 1}}{\sqrt{3 x + 2} \sqrt{5 x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(1/2)/(2+3*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{-2 \, x + 1}}{\sqrt{5 \, x + 3} \sqrt{3 \, x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(-2*x + 1)/(sqrt(5*x + 3)*sqrt(3*x + 2)),x, algorithm="giac")
[Out]