Optimal. Leaf size=116 \[ \frac{3}{20} \sqrt{1-2 x} (5 x+3)^{5/2}+\frac{49 (5 x+3)^{5/2}}{22 \sqrt{1-2 x}}+\frac{14057 \sqrt{1-2 x} (5 x+3)^{3/2}}{1760}+\frac{42171}{640} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{463881 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{640 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.142704, antiderivative size = 116, 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 \[ \frac{3}{20} \sqrt{1-2 x} (5 x+3)^{5/2}+\frac{49 (5 x+3)^{5/2}}{22 \sqrt{1-2 x}}+\frac{14057 \sqrt{1-2 x} (5 x+3)^{3/2}}{1760}+\frac{42171}{640} \sqrt{1-2 x} \sqrt{5 x+3}-\frac{463881 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{640 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 11.5191, size = 105, normalized size = 0.91 \[ \frac{3 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{5}{2}}}{20} + \frac{14057 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}}{1760} + \frac{42171 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{640} - \frac{463881 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{6400} + \frac{49 \left (5 x + 3\right )^{\frac{5}{2}}}{22 \sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)**(3/2)/(1-2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0917007, size = 69, normalized size = 0.59 \[ \frac{463881 \sqrt{10-20 x} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )-10 \sqrt{5 x+3} \left (4800 x^3+18840 x^2+45538 x-71199\right )}{6400 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^2*(3 + 5*x)^(3/2))/(1 - 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.019, size = 123, normalized size = 1.1 \[ -{\frac{1}{-12800+25600\,x} \left ( -96000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+927762\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x-376800\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-463881\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -910760\,x\sqrt{-10\,{x}^{2}-x+3}+1423980\,\sqrt{-10\,{x}^{2}-x+3} \right ) \sqrt{1-2\,x}\sqrt{3+5\,x}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.51225, size = 208, normalized size = 1.79 \[ -\frac{23793}{640} \, \sqrt{5} \sqrt{2} \arcsin \left (\frac{20}{11} \, x + \frac{1}{11}\right ) - \frac{11979}{12800} i \, \sqrt{5} \sqrt{2} \arcsin \left (\frac{20}{11} \, x - \frac{21}{11}\right ) - \frac{3}{8} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{99}{32} \, \sqrt{10 \, x^{2} - 21 \, x + 8} x - \frac{2079}{640} \, \sqrt{10 \, x^{2} - 21 \, x + 8} + \frac{693}{32} \, \sqrt{-10 \, x^{2} - x + 3} - \frac{49 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{21 \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}}}{8 \,{\left (2 \, x - 1\right )}} - \frac{1617 \, \sqrt{-10 \, x^{2} - x + 3}}{16 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^2/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.234871, size = 107, normalized size = 0.92 \[ \frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (4800 \, x^{3} + 18840 \, x^{2} + 45538 \, x - 71199\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 463881 \,{\left (2 \, x - 1\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{12800 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^2/(-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)**2*(3+5*x)**(3/2)/(1-2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.236486, size = 113, normalized size = 0.97 \[ -\frac{463881}{6400} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) + \frac{{\left (2 \,{\left (12 \,{\left (8 \, \sqrt{5}{\left (5 \, x + 3\right )} + 85 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 14057 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} - 463881 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{16000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^2/(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]