Optimal. Leaf size=89 \[ -\frac{1600 \sqrt{1-2 x}}{43923 \sqrt{5 x+3}}-\frac{400 \sqrt{1-2 x}}{3993 (5 x+3)^{3/2}}+\frac{20}{121 (5 x+3)^{3/2} \sqrt{1-2 x}}+\frac{2}{33 (5 x+3)^{3/2} (1-2 x)^{3/2}} \]
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Rubi [A] time = 0.0724173, antiderivative size = 89, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.105 \[ -\frac{1600 \sqrt{1-2 x}}{43923 \sqrt{5 x+3}}-\frac{400 \sqrt{1-2 x}}{3993 (5 x+3)^{3/2}}+\frac{20}{121 (5 x+3)^{3/2} \sqrt{1-2 x}}+\frac{2}{33 (5 x+3)^{3/2} (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 8.36827, size = 80, normalized size = 0.9 \[ - \frac{1600 \sqrt{- 2 x + 1}}{43923 \sqrt{5 x + 3}} - \frac{400 \sqrt{- 2 x + 1}}{3993 \left (5 x + 3\right )^{\frac{3}{2}}} + \frac{20}{121 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}} + \frac{2}{33 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**(5/2)/(3+5*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0416311, size = 37, normalized size = 0.42 \[ \frac{-32000 x^3-4800 x^2+14280 x+722}{43923 (1-2 x)^{3/2} (5 x+3)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)),x]
[Out]
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Maple [A] time = 0.003, size = 32, normalized size = 0.4 \[ -{\frac{32000\,{x}^{3}+4800\,{x}^{2}-14280\,x-722}{43923} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}} \left ( 3+5\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^(5/2)/(3+5*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.34151, size = 80, normalized size = 0.9 \[ \frac{3200 \, x}{43923 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{160}{43923 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{40 \, x}{363 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}} + \frac{2}{363 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.23009, size = 72, normalized size = 0.81 \[ -\frac{2 \,{\left (16000 \, x^{3} + 2400 \, x^{2} - 7140 \, x - 361\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}{43923 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*(-2*x + 1)^(5/2)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 141.072, size = 393, normalized size = 4.42 \[ \begin{cases} - \frac{32000 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )^{3}}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} + \frac{52800 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )^{2}}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} - \frac{14520 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} - \frac{2662 \sqrt{10} \sqrt{-1 + \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} & \text{for}\: \frac{11 \left |{\frac{1}{x + \frac{3}{5}}}\right |}{10} > 1 \\- \frac{32000 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )^{3}}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} + \frac{52800 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )^{2}}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} - \frac{14520 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}} \left (x + \frac{3}{5}\right )}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} - \frac{2662 \sqrt{10} i \sqrt{1 - \frac{11}{10 \left (x + \frac{3}{5}\right )}}}{5314683 x + 4392300 \left (x + \frac{3}{5}\right )^{3} - 9663060 \left (x + \frac{3}{5}\right )^{2} + \frac{15944049}{5}} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**(5/2)/(3+5*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.239323, size = 223, normalized size = 2.51 \[ -\frac{5 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}}{702768 \,{\left (5 \, x + 3\right )}^{\frac{3}{2}}} - \frac{5 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}{5324 \, \sqrt{5 \, x + 3}} - \frac{8 \,{\left (16 \, \sqrt{5}{\left (5 \, x + 3\right )} - 99 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{219615 \,{\left (2 \, x - 1\right )}^{2}} + \frac{5 \,{\left (\frac{33 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} + 4 \, \sqrt{10}\right )}{\left (5 \, x + 3\right )}^{\frac{3}{2}}}{43923 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(5/2)*(-2*x + 1)^(5/2)),x, algorithm="giac")
[Out]