Optimal. Leaf size=179 \[ -\frac{\sqrt{5 x+3} (11603280 x+12923401) (1-2 x)^{7/2}}{22400000}-\frac{3}{70} (3 x+2)^3 \sqrt{5 x+3} (1-2 x)^{7/2}-\frac{271 (3 x+2)^2 \sqrt{5 x+3} (1-2 x)^{7/2}}{2800}+\frac{9526549 \sqrt{5 x+3} (1-2 x)^{5/2}}{96000000}+\frac{104792039 \sqrt{5 x+3} (1-2 x)^{3/2}}{384000000}+\frac{1152712429 \sqrt{5 x+3} \sqrt{1-2 x}}{1280000000}+\frac{12679836719 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{1280000000 \sqrt{10}} \]
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Rubi [A] time = 0.269291, antiderivative size = 179, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ -\frac{\sqrt{5 x+3} (11603280 x+12923401) (1-2 x)^{7/2}}{22400000}-\frac{3}{70} (3 x+2)^3 \sqrt{5 x+3} (1-2 x)^{7/2}-\frac{271 (3 x+2)^2 \sqrt{5 x+3} (1-2 x)^{7/2}}{2800}+\frac{9526549 \sqrt{5 x+3} (1-2 x)^{5/2}}{96000000}+\frac{104792039 \sqrt{5 x+3} (1-2 x)^{3/2}}{384000000}+\frac{1152712429 \sqrt{5 x+3} \sqrt{1-2 x}}{1280000000}+\frac{12679836719 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{1280000000 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/Sqrt[3 + 5*x],x]
[Out]
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Rubi in Sympy [A] time = 24.8109, size = 165, normalized size = 0.92 \[ - \frac{3 \left (- 2 x + 1\right )^{\frac{7}{2}} \left (3 x + 2\right )^{3} \sqrt{5 x + 3}}{70} - \frac{271 \left (- 2 x + 1\right )^{\frac{7}{2}} \left (3 x + 2\right )^{2} \sqrt{5 x + 3}}{2800} - \frac{\left (- 2 x + 1\right )^{\frac{7}{2}} \sqrt{5 x + 3} \left (4351230 x + \frac{38770203}{8}\right )}{8400000} + \frac{9526549 \left (- 2 x + 1\right )^{\frac{5}{2}} \sqrt{5 x + 3}}{96000000} + \frac{104792039 \left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}}{384000000} + \frac{1152712429 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{1280000000} + \frac{12679836719 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{12800000000} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)*(2+3*x)**4/(3+5*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.153632, size = 80, normalized size = 0.45 \[ \frac{10 \sqrt{1-2 x} \sqrt{5 x+3} \left (248832000000 x^6+311731200000 x^5-147923712000 x^4-275707382400 x^3+23172376480 x^2+98827130860 x-920643741\right )-266276571099 \sqrt{10} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{268800000000} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^4)/Sqrt[3 + 5*x],x]
[Out]
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Maple [A] time = 0.015, size = 155, normalized size = 0.9 \[{\frac{1}{537600000000}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 4976640000000\,{x}^{6}\sqrt{-10\,{x}^{2}-x+3}+6234624000000\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}-2958474240000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}-5514147648000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+463447529600\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+266276571099\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) +1976542617200\,x\sqrt{-10\,{x}^{2}-x+3}-18412874820\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.50249, size = 170, normalized size = 0.95 \[ \frac{324}{35} \, \sqrt{-10 \, x^{2} - x + 3} x^{6} + \frac{4059}{350} \, \sqrt{-10 \, x^{2} - x + 3} x^{5} - \frac{192609}{35000} \, \sqrt{-10 \, x^{2} - x + 3} x^{4} - \frac{28719519}{2800000} \, \sqrt{-10 \, x^{2} - x + 3} x^{3} + \frac{144827353}{168000000} \, \sqrt{-10 \, x^{2} - x + 3} x^{2} + \frac{4941356543}{1344000000} \, \sqrt{-10 \, x^{2} - x + 3} x - \frac{12679836719}{25600000000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) - \frac{306881247}{8960000000} \, \sqrt{-10 \, x^{2} - x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^4*(-2*x + 1)^(5/2)/sqrt(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.220093, size = 111, normalized size = 0.62 \[ \frac{1}{537600000000} \, \sqrt{10}{\left (2 \, \sqrt{10}{\left (248832000000 \, x^{6} + 311731200000 \, x^{5} - 147923712000 \, x^{4} - 275707382400 \, x^{3} + 23172376480 \, x^{2} + 98827130860 \, x - 920643741\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 266276571099 \, \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^4*(-2*x + 1)^(5/2)/sqrt(5*x + 3),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((1-2*x)**(5/2)*(2+3*x)**4/(3+5*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.28129, size = 602, normalized size = 3.36 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^4*(-2*x + 1)^(5/2)/sqrt(5*x + 3),x, algorithm="giac")
[Out]