Optimal. Leaf size=143 \[ -\frac{3}{50} \sqrt{1-2 x} (3 x+2) (5 x+3)^{7/2}-\frac{963 \sqrt{1-2 x} (5 x+3)^{7/2}}{4000}-\frac{78167 \sqrt{1-2 x} (5 x+3)^{5/2}}{48000}-\frac{859837 \sqrt{1-2 x} (5 x+3)^{3/2}}{76800}-\frac{9458207 \sqrt{1-2 x} \sqrt{5 x+3}}{102400}+\frac{104040277 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{102400 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.167198, antiderivative size = 143, 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 \[ -\frac{3}{50} \sqrt{1-2 x} (3 x+2) (5 x+3)^{7/2}-\frac{963 \sqrt{1-2 x} (5 x+3)^{7/2}}{4000}-\frac{78167 \sqrt{1-2 x} (5 x+3)^{5/2}}{48000}-\frac{859837 \sqrt{1-2 x} (5 x+3)^{3/2}}{76800}-\frac{9458207 \sqrt{1-2 x} \sqrt{5 x+3}}{102400}+\frac{104040277 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{102400 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^2*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]
[Out]
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Rubi in Sympy [A] time = 13.2658, size = 129, normalized size = 0.9 \[ - \frac{\sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{7}{2}} \left (9 x + 6\right )}{50} - \frac{963 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{7}{2}}}{4000} - \frac{78167 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{5}{2}}}{48000} - \frac{859837 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}}{76800} - \frac{9458207 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{102400} + \frac{104040277 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{1024000} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2*(3+5*x)**(5/2)/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.113895, size = 70, normalized size = 0.49 \[ \frac{-10 \sqrt{1-2 x} \sqrt{5 x+3} \left (6912000 x^4+26294400 x^3+44906720 x^2+48658820 x+46187289\right )-312120831 \sqrt{10} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{3072000} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^2*(3 + 5*x)^(5/2))/Sqrt[1 - 2*x],x]
[Out]
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Maple [A] time = 0.014, size = 121, normalized size = 0.9 \[{\frac{1}{6144000}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( -138240000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}-525888000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}-898134400\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+312120831\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -973176400\,x\sqrt{-10\,{x}^{2}-x+3}-923745780\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.50472, size = 124, normalized size = 0.87 \[ -\frac{45}{2} \, \sqrt{-10 \, x^{2} - x + 3} x^{4} - \frac{2739}{32} \, \sqrt{-10 \, x^{2} - x + 3} x^{3} - \frac{280667}{1920} \, \sqrt{-10 \, x^{2} - x + 3} x^{2} - \frac{2432941}{15360} \, \sqrt{-10 \, x^{2} - x + 3} x - \frac{104040277}{2048000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) - \frac{15395763}{102400} \, \sqrt{-10 \, x^{2} - x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.217994, size = 97, normalized size = 0.68 \[ -\frac{1}{6144000} \, \sqrt{10}{\left (2 \, \sqrt{10}{\left (6912000 \, x^{4} + 26294400 \, x^{3} + 44906720 \, x^{2} + 48658820 \, x + 46187289\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 312120831 \, \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^2/sqrt(-2*x + 1),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)**(5/2)/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.239831, size = 97, normalized size = 0.68 \[ -\frac{1}{15360000} \, \sqrt{5}{\left (2 \,{\left (4 \,{\left (8 \,{\left (36 \,{\left (240 \, x + 481\right )}{\left (5 \, x + 3\right )} + 78167\right )}{\left (5 \, x + 3\right )} + 4299185\right )}{\left (5 \, x + 3\right )} + 141873105\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5} - 1560604155 \, \sqrt{2} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^2/sqrt(-2*x + 1),x, algorithm="giac")
[Out]