Optimal. Leaf size=32 \[ -\frac{2 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{\sqrt{7}} \]
[Out]
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Rubi [A] time = 0.0488416, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077 \[ -\frac{2 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{\sqrt{7}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - 2*x]*(2 + 3*x)*Sqrt[3 + 5*x]),x]
[Out]
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Rubi in Sympy [A] time = 4.74363, size = 34, normalized size = 1.06 \[ - \frac{2 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(2+3*x)/(1-2*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0443496, size = 35, normalized size = 1.09 \[ -\frac{\tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{\sqrt{7}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)*Sqrt[3 + 5*x]),x]
[Out]
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Maple [B] time = 0.017, size = 55, normalized size = 1.7 \[{\frac{\sqrt{7}}{7}\sqrt{1-2\,x}\sqrt{3+5\,x}\arctan \left ({\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{14}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2+3*x)/(1-2*x)^(1/2)/(3+5*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.4999, size = 38, normalized size = 1.19 \[ \frac{1}{7} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*(3*x + 2)*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224452, size = 41, normalized size = 1.28 \[ \frac{1}{7} \, \sqrt{7} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*(3*x + 2)*sqrt(-2*x + 1)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- 2 x + 1} \left (3 x + 2\right ) \sqrt{5 x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(2+3*x)/(1-2*x)**(1/2)/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.231936, size = 99, normalized size = 3.09 \[ \frac{1}{70} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(5*x + 3)*(3*x + 2)*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]