Optimal. Leaf size=142 \[ \frac{\sqrt{5 x+3} (3 x+2)^4}{3 (1-2 x)^{3/2}}-\frac{299 \sqrt{5 x+3} (3 x+2)^3}{66 \sqrt{1-2 x}}-\frac{697}{88} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (7306140 x+17606479)}{70400}+\frac{13246251 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{6400 \sqrt{10}} \]
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Rubi [A] time = 0.258207, antiderivative size = 142, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{\sqrt{5 x+3} (3 x+2)^4}{3 (1-2 x)^{3/2}}-\frac{299 \sqrt{5 x+3} (3 x+2)^3}{66 \sqrt{1-2 x}}-\frac{697}{88} \sqrt{1-2 x} \sqrt{5 x+3} (3 x+2)^2-\frac{\sqrt{1-2 x} \sqrt{5 x+3} (7306140 x+17606479)}{70400}+\frac{13246251 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{6400 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^4*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]
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Rubi in Sympy [A] time = 26.9749, size = 131, normalized size = 0.92 \[ - \frac{697 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{2} \sqrt{5 x + 3}}{88} - \frac{\sqrt{- 2 x + 1} \sqrt{5 x + 3} \left (\frac{82194075 x}{4} + \frac{792291555}{16}\right )}{198000} + \frac{13246251 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{64000} - \frac{299 \left (3 x + 2\right )^{3} \sqrt{5 x + 3}}{66 \sqrt{- 2 x + 1}} + \frac{\left (3 x + 2\right )^{4} \sqrt{5 x + 3}}{3 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**4*(3+5*x)**(1/2)/(1-2*x)**(5/2),x)
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Mathematica [A] time = 0.176014, size = 79, normalized size = 0.56 \[ \frac{437126283 \sqrt{10-20 x} (2 x-1) \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )-10 \sqrt{5 x+3} \left (2851200 x^4+15040080 x^3+52700868 x^2-183672928 x+66038637\right )}{2112000 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^4*Sqrt[3 + 5*x])/(1 - 2*x)^(5/2),x]
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Maple [A] time = 0.022, size = 154, normalized size = 1.1 \[{\frac{1}{4224000\, \left ( -1+2\,x \right ) ^{2}} \left ( -57024000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}+1748505132\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ){x}^{2}-300801600\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}-1748505132\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x-1054017360\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+437126283\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) +3673458560\,x\sqrt{-10\,{x}^{2}-x+3}-1320772740\,\sqrt{-10\,{x}^{2}-x+3} \right ) \sqrt{1-2\,x}\sqrt{3+5\,x}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^4*(3+5*x)^(1/2)/(1-2*x)^(5/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="maxima")
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Fricas [A] time = 0.228946, size = 127, normalized size = 0.89 \[ -\frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (2851200 \, x^{4} + 15040080 \, x^{3} + 52700868 \, x^{2} - 183672928 \, x + 66038637\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 437126283 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{4224000 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="fricas")
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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)**4*(3+5*x)**(1/2)/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.237615, size = 131, normalized size = 0.92 \[ \frac{13246251}{64000} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) - \frac{{\left (4 \,{\left (891 \,{\left (4 \,{\left (8 \, \sqrt{5}{\left (5 \, x + 3\right )} + 115 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 8919 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} - 291417650 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 4808389113 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{26400000 \,{\left (2 \, x - 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(5*x + 3)*(3*x + 2)^4/(-2*x + 1)^(5/2),x, algorithm="giac")
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