Optimal. Leaf size=45 \[ -\frac{8 \sqrt{1-2 x}}{363 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x}}{33 (5 x+3)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0325141, antiderivative size = 45, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{8 \sqrt{1-2 x}}{363 \sqrt{5 x+3}}-\frac{2 \sqrt{1-2 x}}{33 (5 x+3)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 4.3171, size = 41, normalized size = 0.91 \[ - \frac{8 \sqrt{- 2 x + 1}}{363 \sqrt{5 x + 3}} - \frac{2 \sqrt{- 2 x + 1}}{33 \left (5 x + 3\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(3+5*x)**(5/2)/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0230932, size = 27, normalized size = 0.6 \[ -\frac{2 \sqrt{1-2 x} (20 x+23)}{363 (5 x+3)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - 2*x]*(3 + 5*x)^(5/2)),x]
[Out]
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Maple [A] time = 0.004, size = 22, normalized size = 0.5 \[ -{\frac{46+40\,x}{363}\sqrt{1-2\,x} \left ( 3+5\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(3+5*x)^(5/2)/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.49888, size = 65, normalized size = 1.44 \[ -\frac{2 \, \sqrt{-10 \, x^{2} - x + 3}}{33 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} - \frac{8 \, \sqrt{-10 \, x^{2} - x + 3}}{363 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.214481, size = 45, normalized size = 1. \[ -\frac{2 \,{\left (20 \, x + 23\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{363 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*sqrt(-2*x + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 8.11816, size = 104, normalized size = 2.31 \[ \begin{cases} - \frac{8 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{1815} - \frac{2 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{825 \left (x + \frac{3}{5}\right )} & \text{for}\: \frac{11 \left |{\frac{1}{x + \frac{3}{5}}}\right |}{10} > 1 \\- \frac{8 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{1815} - \frac{2 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{825 \left (x + \frac{3}{5}\right )} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(3+5*x)**(5/2)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.233517, size = 170, normalized size = 3.78 \[ -\frac{\sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}}{29040 \,{\left (5 \, x + 3\right )}^{\frac{3}{2}}} - \frac{3 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}{2420 \, \sqrt{5 \, x + 3}} + \frac{{\left (\frac{9 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} + 4 \, \sqrt{10}\right )}{\left (5 \, x + 3\right )}^{\frac{3}{2}}}{1815 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]