Optimal. Leaf size=67 \[ -\frac{160 \sqrt{1-2 x}}{3993 \sqrt{5 x+3}}-\frac{40 \sqrt{1-2 x}}{363 (5 x+3)^{3/2}}+\frac{2}{11 (5 x+3)^{3/2} \sqrt{1-2 x}} \]
[Out]
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Rubi [A] time = 0.0508741, antiderivative size = 67, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{160 \sqrt{1-2 x}}{3993 \sqrt{5 x+3}}-\frac{40 \sqrt{1-2 x}}{363 (5 x+3)^{3/2}}+\frac{2}{11 (5 x+3)^{3/2} \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 5.9186, size = 60, normalized size = 0.9 \[ - \frac{160 \sqrt{- 2 x + 1}}{3993 \sqrt{5 x + 3}} - \frac{40 \sqrt{- 2 x + 1}}{363 \left (5 x + 3\right )^{\frac{3}{2}}} + \frac{2}{11 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**(3/2)/(3+5*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0304998, size = 32, normalized size = 0.48 \[ \frac{2 \left (800 x^2+520 x-97\right )}{3993 \sqrt{1-2 x} (5 x+3)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]
[Out]
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Maple [A] time = 0.005, size = 27, normalized size = 0.4 \[{\frac{1600\,{x}^{2}+1040\,x-194}{3993} \left ( 3+5\,x \right ) ^{-{\frac{3}{2}}}{\frac{1}{\sqrt{1-2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^(3/2)/(3+5*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.3544, size = 86, normalized size = 1.28 \[ \frac{320 \, x}{3993 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{16}{3993 \, \sqrt{-10 \, x^{2} - x + 3}} - \frac{2}{33 \,{\left (5 \, \sqrt{-10 \, x^{2} - x + 3} x + 3 \, \sqrt{-10 \, x^{2} - x + 3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224411, size = 58, normalized size = 0.87 \[ -\frac{2 \,{\left (800 \, x^{2} + 520 \, x - 97\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{3993 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*(-2*x + 1)^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 40.047, size = 231, normalized size = 3.45 \[ \begin{cases} - \frac{1600 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )^{2}}{- 219615 x + 199650 \left (x + \frac{3}{5}\right )^{2} - 131769} + \frac{880 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )}{- 219615 x + 199650 \left (x + \frac{3}{5}\right )^{2} - 131769} + \frac{242 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{- 219615 x + 199650 \left (x + \frac{3}{5}\right )^{2} - 131769} & \text{for}\: \frac{11 \left |{\frac{1}{x + \frac{3}{5}}}\right |}{10} > 1 \\- \frac{1600 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )^{2}}{- 219615 x + 199650 \left (x + \frac{3}{5}\right )^{2} - 131769} + \frac{880 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )}{- 219615 x + 199650 \left (x + \frac{3}{5}\right )^{2} - 131769} + \frac{242 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{- 219615 x + 199650 \left (x + \frac{3}{5}\right )^{2} - 131769} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**(3/2)/(3+5*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.235631, size = 205, normalized size = 3.06 \[ -\frac{\sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}}{63888 \,{\left (5 \, x + 3\right )}^{\frac{3}{2}}} - \frac{7 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}{5324 \, \sqrt{5 \, x + 3}} - \frac{8 \, \sqrt{5} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{6655 \,{\left (2 \, x - 1\right )}} + \frac{{\left (\frac{21 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} + 4 \, \sqrt{10}\right )}{\left (5 \, x + 3\right )}^{\frac{3}{2}}}{3993 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]