Optimal. Leaf size=110 \[ \frac{\sqrt{5 x+3} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{7}{4} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2+\frac{\sqrt{1-2 x} \sqrt{5 x+3} (73380 x+176833)}{3200}-\frac{1463447 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{3200 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.184084, antiderivative size = 110, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.192 \[ \frac{\sqrt{5 x+3} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{7}{4} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2+\frac{\sqrt{1-2 x} \sqrt{5 x+3} (73380 x+176833)}{3200}-\frac{1463447 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{3200 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 18.7885, size = 102, normalized size = 0.93 \[ \frac{7 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{2} \sqrt{5 x + 3}}{4} + \frac{\sqrt{- 2 x + 1} \sqrt{5 x + 3} \left (\frac{275175 x}{2} + \frac{2652495}{8}\right )}{6000} - \frac{1463447 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{32000} + \frac{\left (3 x + 2\right )^{3} \sqrt{5 x + 3}}{\sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)**(1/2)/(1-2*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.0928808, size = 69, normalized size = 0.63 \[ \frac{1463447 \sqrt{10-20 x} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )-10 \sqrt{5 x+3} \left (14400 x^3+57960 x^2+142686 x-224833\right )}{32000 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*Sqrt[3 + 5*x])/(1 - 2*x)^(3/2),x]
[Out]
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Maple [A] time = 0.017, size = 123, normalized size = 1.1 \[ -{\frac{1}{-64000+128000\,x} \left ( -288000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+2926894\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x-1159200\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-1463447\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -2853720\,x\sqrt{-10\,{x}^{2}-x+3}+4496660\,\sqrt{-10\,{x}^{2}-x+3} \right ) \sqrt{1-2\,x}\sqrt{3+5\,x}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)^(1/2)/(1-2*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.51689, size = 107, normalized size = 0.97 \[ -\frac{1463447}{64000} \, \sqrt{5} \sqrt{2} \arcsin \left (\frac{20}{11} \, x + \frac{1}{11}\right ) - \frac{9}{40} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{1593}{160} \, \sqrt{-10 \, x^{2} - x + 3} x + \frac{89793}{3200} \, \sqrt{-10 \, x^{2} - x + 3} - \frac{343 \, \sqrt{-10 \, x^{2} - x + 3}}{8 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223108, size = 107, normalized size = 0.97 \[ \frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (14400 \, x^{3} + 57960 \, x^{2} + 142686 \, x - 224833\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 1463447 \,{\left (2 \, x - 1\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{64000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*(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)**(1/2)/(1-2*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.230721, size = 113, normalized size = 1.03 \[ -\frac{1463447}{32000} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) + \frac{{\left (18 \,{\left (4 \,{\left (8 \, \sqrt{5}{\left (5 \, x + 3\right )} + 89 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 4927 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} - 1463447 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{80000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]