Optimal. Leaf size=132 \[ \frac{(5 x+3)^{3/2} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{27}{16} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^2+\frac{9 \sqrt{1-2 x} (5 x+3)^{3/2} (29320 x+62091)}{12800}+\frac{13246251 \sqrt{1-2 x} \sqrt{5 x+3}}{51200}-\frac{145708761 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{51200 \sqrt{10}} \]
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Rubi [A] time = 0.200653, antiderivative size = 132, 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 \[ \frac{(5 x+3)^{3/2} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{27}{16} \sqrt{1-2 x} (5 x+3)^{3/2} (3 x+2)^2+\frac{9 \sqrt{1-2 x} (5 x+3)^{3/2} (29320 x+62091)}{12800}+\frac{13246251 \sqrt{1-2 x} \sqrt{5 x+3}}{51200}-\frac{145708761 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{51200 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 20.295, size = 121, normalized size = 0.92 \[ \frac{27 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{2} \left (5 x + 3\right )^{\frac{3}{2}}}{16} + \frac{\sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}} \left (494775 x + \frac{8382285}{8}\right )}{24000} + \frac{13246251 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{51200} - \frac{145708761 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{512000} + \frac{\left (3 x + 2\right )^{3} \left (5 x + 3\right )^{\frac{3}{2}}}{\sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)**(3/2)/(1-2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.109131, size = 74, normalized size = 0.56 \[ \frac{145708761 \sqrt{10-20 x} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )-10 \sqrt{5 x+3} \left (864000 x^4+3729600 x^3+8057880 x^2+15218818 x-22217679\right )}{512000 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.02, size = 140, normalized size = 1.1 \[ -{\frac{1}{-1024000+2048000\,x} \left ( -17280000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}-74592000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+291417522\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x-161157600\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-145708761\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -304376360\,x\sqrt{-10\,{x}^{2}-x+3}+444353580\,\sqrt{-10\,{x}^{2}-x+3} \right ) \sqrt{1-2\,x}\sqrt{3+5\,x}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.51875, size = 248, normalized size = 1.88 \[ -\frac{27}{32} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x - \frac{155771121}{1024000} \, \sqrt{5} \sqrt{2} \arcsin \left (\frac{20}{11} \, x + \frac{1}{11}\right ) - \frac{251559}{25600} i \, \sqrt{5} \sqrt{2} \arcsin \left (\frac{20}{11} \, x - \frac{21}{11}\right ) - \frac{2547}{640} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{2079}{64} \, \sqrt{10 \, x^{2} - 21 \, x + 8} x - \frac{9801}{2560} \, \sqrt{-10 \, x^{2} - x + 3} x - \frac{43659}{1280} \, \sqrt{10 \, x^{2} - 21 \, x + 8} + \frac{5811399}{51200} \, \sqrt{-10 \, x^{2} - x + 3} - \frac{343 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{441 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{32 \,{\left (2 \, x - 1\right )}} - \frac{11319 \, \sqrt{-10 \, x^{2} - x + 3}}{32 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.233909, size = 113, normalized size = 0.86 \[ \frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (864000 \, x^{4} + 3729600 \, x^{3} + 8057880 \, x^{2} + 15218818 \, x - 22217679\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 145708761 \,{\left (2 \, x - 1\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{1024000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)**(3/2)/(1-2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.238735, size = 131, normalized size = 0.99 \[ -\frac{145708761}{512000} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) + \frac{{\left (2 \,{\left (36 \,{\left (8 \,{\left (12 \, \sqrt{5}{\left (5 \, x + 3\right )} + 115 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 8919 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 4415417 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} - 145708761 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{1280000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="giac")
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