Optimal. Leaf size=84 \[ \frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{\sqrt{1-2 x} (38770 x+24439)}{99825 (5 x+3)^{3/2}}-\frac{27 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{25 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.123076, antiderivative size = 84, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ \frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} (5 x+3)^{3/2}}-\frac{\sqrt{1-2 x} (38770 x+24439)}{99825 (5 x+3)^{3/2}}-\frac{27 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{25 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]
[Out]
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Rubi in Sympy [A] time = 12.3331, size = 80, normalized size = 0.95 \[ - \frac{4 \sqrt{- 2 x + 1} \left (\frac{19385 x}{2} + \frac{24439}{4}\right )}{99825 \left (5 x + 3\right )^{\frac{3}{2}}} - \frac{27 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{250} + \frac{7 \left (3 x + 2\right )^{2}}{11 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3/(1-2*x)**(3/2)/(3+5*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.19352, size = 60, normalized size = 0.71 \[ \frac{649265 x^2+772408 x+229661}{99825 \sqrt{1-2 x} (5 x+3)^{3/2}}+\frac{27 \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{25 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)),x]
[Out]
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Maple [B] time = 0.021, size = 134, normalized size = 1.6 \[ -{\frac{1}{-1996500+3993000\,x}\sqrt{1-2\,x} \left ( 5390550\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ){x}^{3}+3773385\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ){x}^{2}-1293732\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x+12985300\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-970299\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) +15448160\,x\sqrt{-10\,{x}^{2}-x+3}+4593220\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}} \left ( 3+5\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.50419, size = 105, normalized size = 1.25 \[ -\frac{27}{500} \, \sqrt{5} \sqrt{2} \arcsin \left (\frac{20}{11} \, x + \frac{1}{11}\right ) + \frac{129853 \, x}{99825 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{382849}{499125 \, \sqrt{-10 \, x^{2} - x + 3}} - \frac{2}{4125 \,{\left (5 \, \sqrt{-10 \, x^{2} - x + 3} x + 3 \, \sqrt{-10 \, x^{2} - x + 3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^(5/2)*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229976, size = 127, normalized size = 1.51 \[ -\frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (649265 \, x^{2} + 772408 \, x + 229661\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} + 107811 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{1996500 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^(5/2)*(-2*x + 1)^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{3}}{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3/(1-2*x)**(3/2)/(3+5*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.267805, size = 230, normalized size = 2.74 \[ -\frac{\sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}}{7986000 \,{\left (5 \, x + 3\right )}^{\frac{3}{2}}} - \frac{27}{250} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) - \frac{41 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}{133100 \, \sqrt{5 \, x + 3}} - \frac{343 \, \sqrt{5} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{6655 \,{\left (2 \, x - 1\right )}} + \frac{{\left (\frac{615 \, \sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{2}}{5 \, x + 3} + 4 \, \sqrt{10}\right )}{\left (5 \, x + 3\right )}^{\frac{3}{2}}}{499125 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^(5/2)*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]