Optimal. Leaf size=115 \[ -\frac{90415 \sqrt{1-2 x}}{2156 \sqrt{5 x+3}}+\frac{543 \sqrt{1-2 x}}{196 (3 x+2) \sqrt{5 x+3}}+\frac{3 \sqrt{1-2 x}}{14 (3 x+2)^2 \sqrt{5 x+3}}+\frac{56421 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{196 \sqrt{7}} \]
[Out]
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Rubi [A] time = 0.241999, antiderivative size = 115, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{90415 \sqrt{1-2 x}}{2156 \sqrt{5 x+3}}+\frac{543 \sqrt{1-2 x}}{196 (3 x+2) \sqrt{5 x+3}}+\frac{3 \sqrt{1-2 x}}{14 (3 x+2)^2 \sqrt{5 x+3}}+\frac{56421 \tan ^{-1}\left (\frac{\sqrt{1-2 x}}{\sqrt{7} \sqrt{5 x+3}}\right )}{196 \sqrt{7}} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 21.2501, size = 105, normalized size = 0.91 \[ - \frac{90415 \sqrt{- 2 x + 1}}{2156 \sqrt{5 x + 3}} + \frac{543 \sqrt{- 2 x + 1}}{196 \left (3 x + 2\right ) \sqrt{5 x + 3}} + \frac{3 \sqrt{- 2 x + 1}}{14 \left (3 x + 2\right )^{2} \sqrt{5 x + 3}} + \frac{56421 \sqrt{7} \operatorname{atan}{\left (\frac{\sqrt{7} \sqrt{- 2 x + 1}}{7 \sqrt{5 x + 3}} \right )}}{1372} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(2+3*x)**3/(3+5*x)**(3/2)/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0915852, size = 77, normalized size = 0.67 \[ \frac{56421 \tan ^{-1}\left (\frac{-37 x-20}{2 \sqrt{7-14 x} \sqrt{5 x+3}}\right )}{392 \sqrt{7}}-\frac{\sqrt{1-2 x} \left (813735 x^2+1067061 x+349252\right )}{2156 (3 x+2)^2 \sqrt{5 x+3}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2)),x]
[Out]
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Maple [B] time = 0.023, size = 202, normalized size = 1.8 \[ -{\frac{1}{30184\, \left ( 2+3\,x \right ) ^{2}} \left ( 27928395\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{3}+53994897\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ){x}^{2}+34755336\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) x+11392290\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+7447572\,\sqrt{7}\arctan \left ( 1/14\,{\frac{ \left ( 37\,x+20 \right ) \sqrt{7}}{\sqrt{-10\,{x}^{2}-x+3}}} \right ) +14938854\,x\sqrt{-10\,{x}^{2}-x+3}+4889528\,\sqrt{-10\,{x}^{2}-x+3} \right ) \sqrt{1-2\,x}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}{\frac{1}{\sqrt{3+5\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2+3*x)^3/(3+5*x)^(3/2)/(1-2*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (5 \, x + 3\right )}^{\frac{3}{2}}{\left (3 \, x + 2\right )}^{3} \sqrt{-2 \, x + 1}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^3*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233186, size = 127, normalized size = 1.1 \[ -\frac{\sqrt{7}{\left (2 \, \sqrt{7}{\left (813735 \, x^{2} + 1067061 \, x + 349252\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 620631 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \arctan \left (\frac{\sqrt{7}{\left (37 \, x + 20\right )}}{14 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{30184 \,{\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^3*sqrt(-2*x + 1)),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/(2+3*x)**3/(3+5*x)**(3/2)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.292462, size = 427, normalized size = 3.71 \[ -\frac{56421}{27440} \, \sqrt{70} \sqrt{10}{\left (\pi + 2 \, \arctan \left (-\frac{\sqrt{70} \sqrt{5 \, x + 3}{\left (\frac{{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} - 4\right )}}{140 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}\right )\right )} - \frac{25}{22} \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )} - \frac{297 \,{\left (107 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{3} + 23800 \, \sqrt{10}{\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}\right )}}{98 \,{\left ({\left (\frac{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}{\sqrt{5 \, x + 3}} - \frac{4 \, \sqrt{5 \, x + 3}}{\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}}\right )}^{2} + 280\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^3*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]