Optimal. Leaf size=108 \[ -\frac{17735 \sqrt{1-2 x}}{5929 \sqrt{5 x+3}}-\frac{58}{539 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{3}{7 \sqrt{1-2 x} (3 x+2) \sqrt{5 x+3}}+\frac{999 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{49 \sqrt{7}} \]
[Out]
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Rubi [A] time = 0.251875, antiderivative size = 108, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.192 \[ -\frac{17735 \sqrt{1-2 x}}{5929 \sqrt{5 x+3}}-\frac{58}{539 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{3}{7 \sqrt{1-2 x} (3 x+2) \sqrt{5 x+3}}+\frac{999 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{49 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 22.1975, size = 99, normalized size = 0.92 \[ - \frac{17735 \sqrt{- 2 x + 1}}{5929 \sqrt{5 x + 3}} + \frac{999 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{343} - \frac{58}{539 \sqrt{- 2 x + 1} \sqrt{5 x + 3}} + \frac{3}{7 \sqrt{- 2 x + 1} \left (3 x + 2\right ) \sqrt{5 x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**(3/2)/(2+3*x)**2/(3+5*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.100253, size = 80, normalized size = 0.74 \[ \frac{999 \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{98 \sqrt{7}}-\frac{\sqrt{1-2 x} \left (106410 x^2+15821 x-34205\right )}{5929 \sqrt{5 x+3} \left (6 x^2+x-2\right )} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(3/2)),x]
[Out]
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Maple [B] time = 0.023, size = 209, normalized size = 1.9 \[ -{\frac{1}{ \left ( 166012+249018\,x \right ) \left ( -1+2\,x \right ) }\sqrt{1-2\,x} \left ( 3626370\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}+2780217\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}-846153\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+1489740\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-725274\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) +221494\,x\sqrt{-10\,{x}^{2}-x+3}-478870\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}{\frac{1}{\sqrt{3+5\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^(3/2)/(2+3*x)^2/(3+5*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.51323, size = 124, normalized size = 1.15 \[ -\frac{999}{686} \, \sqrt{7} \arcsin \left (\frac{37 \, x}{11 \,{\left | 3 \, x + 2 \right |}} + \frac{20}{11 \,{\left | 3 \, x + 2 \right |}}\right ) + \frac{35470 \, x}{5929 \, \sqrt{-10 \, x^{2} - x + 3}} - \frac{18373}{5929 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{3}{7 \,{\left (3 \, \sqrt{-10 \, x^{2} - x + 3} x + 2 \, \sqrt{-10 \, x^{2} - x + 3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^2*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.235831, size = 127, normalized size = 1.18 \[ -\frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (106410 \, x^{2} + 15821 \, x - 34205\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 120879 \,{\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{83006 \,{\left (30 \, x^{3} + 23 \, x^{2} - 7 \, x - 6\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^2*(-2*x + 1)^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**(3/2)/(2+3*x)**2/(3+5*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.311981, size = 375, normalized size = 3.47 \[ -\frac{999}{6860} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} - \frac{25}{242} \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )} - \frac{16 \, \sqrt{5} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{29645 \,{\left (2 \, x - 1\right )}} - \frac{594 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}}{49 \,{\left ({\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{2} + 280\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^2*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]