Optimal. Leaf size=128 \[ -\frac{3}{50} \sqrt{1-2 x} (3 x+2)^2 (5 x+3)^{5/2}-\frac{3 \sqrt{1-2 x} (3900 x+7889) (5 x+3)^{5/2}}{16000}-\frac{917953 \sqrt{1-2 x} (5 x+3)^{3/2}}{128000}-\frac{30292449 \sqrt{1-2 x} \sqrt{5 x+3}}{512000}+\frac{333216939 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{512000 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.163333, antiderivative size = 128, 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 \[ -\frac{3}{50} \sqrt{1-2 x} (3 x+2)^2 (5 x+3)^{5/2}-\frac{3 \sqrt{1-2 x} (3900 x+7889) (5 x+3)^{5/2}}{16000}-\frac{917953 \sqrt{1-2 x} (5 x+3)^{3/2}}{128000}-\frac{30292449 \sqrt{1-2 x} \sqrt{5 x+3}}{512000}+\frac{333216939 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{512000 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 15.3677, size = 117, normalized size = 0.91 \[ - \frac{3 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{2} \left (5 x + 3\right )^{\frac{5}{2}}}{50} - \frac{\sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{5}{2}} \left (43875 x + \frac{355005}{4}\right )}{60000} - \frac{917953 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}}{128000} - \frac{30292449 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{512000} + \frac{333216939 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{5120000} \]
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)**(1/2),x)
[Out]
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Mathematica [A] time = 0.11692, size = 70, normalized size = 0.55 \[ \frac{-10 \sqrt{1-2 x} \sqrt{5 x+3} \left (6912000 x^4+26870400 x^3+46785120 x^2+51453140 x+49229901\right )-333216939 \sqrt{10} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{5120000} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x)^(3/2))/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.013, size = 121, normalized size = 1. \[{\frac{1}{10240000}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( -138240000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}-537408000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}-935702400\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+333216939\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -1029062800\,x\sqrt{-10\,{x}^{2}-x+3}-984598020\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.50205, size = 124, normalized size = 0.97 \[ -\frac{27}{2} \, \sqrt{-10 \, x^{2} - x + 3} x^{4} - \frac{8397}{160} \, \sqrt{-10 \, x^{2} - x + 3} x^{3} - \frac{292407}{3200} \, \sqrt{-10 \, x^{2} - x + 3} x^{2} - \frac{2572657}{25600} \, \sqrt{-10 \, x^{2} - x + 3} x - \frac{333216939}{10240000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) - \frac{49229901}{512000} \, \sqrt{-10 \, x^{2} - x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216733, size = 97, normalized size = 0.76 \[ -\frac{1}{10240000} \, \sqrt{10}{\left (2 \, \sqrt{10}{\left (6912000 \, x^{4} + 26870400 \, x^{3} + 46785120 \, x^{2} + 51453140 \, x + 49229901\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 333216939 \, \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="fricas")
[Out]
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Sympy [A] time = 98.4051, size = 597, normalized size = 4.66 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3*(3+5*x)**(3/2)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.246283, size = 97, normalized size = 0.76 \[ -\frac{1}{25600000} \, \sqrt{5}{\left (2 \,{\left (4 \,{\left (24 \,{\left (36 \,{\left (80 \, x + 167\right )}{\left (5 \, x + 3\right )} + 27809\right )}{\left (5 \, x + 3\right )} + 4589765\right )}{\left (5 \, x + 3\right )} + 151462245\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5} - 1666084695 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(3/2)*(3*x + 2)^3/sqrt(-2*x + 1),x, algorithm="giac")
[Out]