Optimal. Leaf size=150 \[ -\frac{1}{20} (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{5/2}-\frac{7 (1-2 x)^{3/2} (2256 x+3821) (5 x+3)^{5/2}}{32000}-\frac{953981 (1-2 x)^{3/2} (5 x+3)^{3/2}}{384000}-\frac{10493791 (1-2 x)^{3/2} \sqrt{5 x+3}}{1024000}+\frac{115431701 \sqrt{1-2 x} \sqrt{5 x+3}}{10240000}+\frac{1269748711 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{10240000 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.18408, antiderivative size = 150, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 5, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.192 \[ -\frac{1}{20} (1-2 x)^{3/2} (3 x+2)^2 (5 x+3)^{5/2}-\frac{7 (1-2 x)^{3/2} (2256 x+3821) (5 x+3)^{5/2}}{32000}-\frac{953981 (1-2 x)^{3/2} (5 x+3)^{3/2}}{384000}-\frac{10493791 (1-2 x)^{3/2} \sqrt{5 x+3}}{1024000}+\frac{115431701 \sqrt{1-2 x} \sqrt{5 x+3}}{10240000}+\frac{1269748711 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{10240000 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]
[Out]
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Rubi in Sympy [A] time = 16.525, size = 136, normalized size = 0.91 \[ - \frac{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (3 x + 2\right )^{2} \left (5 x + 3\right )^{\frac{5}{2}}}{20} - \frac{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{5}{2}} \left (59220 x + \frac{401205}{4}\right )}{120000} + \frac{953981 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{5}{2}}}{960000} - \frac{10493791 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}}{7680000} - \frac{115431701 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{10240000} + \frac{1269748711 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{102400000} \]
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 = 0.119117, size = 75, normalized size = 0.5 \[ \frac{10 \sqrt{1-2 x} \sqrt{5 x+3} \left (691200000 x^5+2163456000 x^4+2600899200 x^3+1349400160 x^2+21761620 x-483864147\right )-3809246133 \sqrt{10} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{307200000} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]
[Out]
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Maple [A] time = 0.013, size = 138, normalized size = 0.9 \[{\frac{1}{614400000}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 13824000000\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}+43269120000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}+52017984000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+26988003200\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+3809246133\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) +435232400\,x\sqrt{-10\,{x}^{2}-x+3}-9677282940\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
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 = 1.49218, size = 140, normalized size = 0.93 \[ -\frac{9}{4} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{3} - \frac{2727}{400} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{2} - \frac{270711}{32000} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x - \frac{2147273}{384000} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{10493791}{512000} \, \sqrt{-10 \, x^{2} - x + 3} x - \frac{1269748711}{204800000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) + \frac{10493791}{10240000} \, \sqrt{-10 \, x^{2} - x + 3} \]
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 = 0.221153, size = 104, normalized size = 0.69 \[ \frac{1}{614400000} \, \sqrt{10}{\left (2 \, \sqrt{10}{\left (691200000 \, x^{5} + 2163456000 \, x^{4} + 2600899200 \, x^{3} + 1349400160 \, x^{2} + 21761620 \, x - 483864147\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 3809246133 \, \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )} \]
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 = 48.1956, size = 694, normalized size = 4.63 \[ \text{result too large to display} \]
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 = 0.267317, size = 427, normalized size = 2.85 \[ \frac{9}{512000000} \, \sqrt{5}{\left (2 \,{\left (4 \,{\left (8 \,{\left (4 \,{\left (16 \,{\left (100 \, x - 239\right )}{\left (5 \, x + 3\right )} + 27999\right )}{\left (5 \, x + 3\right )} - 318159\right )}{\left (5 \, x + 3\right )} + 3237255\right )}{\left (5 \, x + 3\right )} - 2656665\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5} + 29223315 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right )\right )} + \frac{117}{64000000} \, \sqrt{5}{\left (2 \,{\left (4 \,{\left (8 \,{\left (12 \,{\left (80 \, x - 143\right )}{\left (5 \, x + 3\right )} + 9773\right )}{\left (5 \, x + 3\right )} - 136405\right )}{\left (5 \, x + 3\right )} + 60555\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5} - 666105 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right )\right )} + \frac{57}{320000} \, \sqrt{5}{\left (2 \,{\left (4 \,{\left (8 \,{\left (60 \, x - 71\right )}{\left (5 \, x + 3\right )} + 2179\right )}{\left (5 \, x + 3\right )} - 4125\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5} + 45375 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right )\right )} + \frac{37}{6000} \, \sqrt{5}{\left (2 \,{\left (4 \,{\left (40 \, x - 23\right )}{\left (5 \, x + 3\right )} + 33\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5} - 363 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right )\right )} + \frac{3}{50} \, \sqrt{5}{\left (2 \,{\left (20 \, x + 1\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5} + 121 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right )\right )} \]
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]