Optimal. Leaf size=84 \[ \frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{\sqrt{1-2 x} (50985 x+30443)}{12100 \sqrt{5 x+3}}-\frac{999 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{100 \sqrt{10}} \]
[Out]
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Rubi [A] time = 0.122271, 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 \[ \frac{7 (3 x+2)^2}{11 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{\sqrt{1-2 x} (50985 x+30443)}{12100 \sqrt{5 x+3}}-\frac{999 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{100 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 11.8214, size = 78, normalized size = 0.93 \[ \frac{\sqrt{- 2 x + 1} \left (\frac{50985 x}{4} + \frac{30443}{4}\right )}{3025 \sqrt{5 x + 3}} - \frac{999 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{1000} + \frac{7 \left (3 x + 2\right )^{2}}{11 \sqrt{- 2 x + 1} \sqrt{5 x + 3}} \]
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)**(3/2),x)
[Out]
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Mathematica [A] time = 0.13241, size = 70, normalized size = 0.83 \[ \frac{-326700 x^2+824990 x+120879 \sqrt{10-20 x} \sqrt{5 x+3} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )+612430}{121000 \sqrt{1-2 x} \sqrt{5 x+3}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*(3 + 5*x)^(3/2)),x]
[Out]
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Maple [A] time = 0.02, size = 120, normalized size = 1.4 \[ -{\frac{1}{-242000+484000\,x}\sqrt{1-2\,x} \left ( 1208790\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ){x}^{2}+120879\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x-653400\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-362637\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) +1649980\,x\sqrt{-10\,{x}^{2}-x+3}+1224860\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}{\frac{1}{\sqrt{3+5\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^(3/2),x)
[Out]
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Maxima [A] time = 1.49957, size = 78, normalized size = 0.93 \[ -\frac{27 \, x^{2}}{10 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{999}{2000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) + \frac{82499 \, x}{12100 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{61243}{12100 \, \sqrt{-10 \, x^{2} - x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^(3/2)*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.236266, size = 108, normalized size = 1.29 \[ \frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (32670 \, x^{2} - 82499 \, x - 61243\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 120879 \,{\left (10 \, x^{2} + x - 3\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{242000 \,{\left (10 \, x^{2} + x - 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^(3/2)*(-2*x + 1)^(3/2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{3}}{\left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{\frac{3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3/(1-2*x)**(3/2)/(3+5*x)**(3/2),x)
[Out]
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GIAC/XCAS [A] time = 0.250225, size = 159, normalized size = 1.89 \[ -\frac{999}{1000} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) + \frac{{\left (6534 \, \sqrt{5}{\left (5 \, x + 3\right )} - 121687 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{302500 \,{\left (2 \, x - 1\right )}} - \frac{\sqrt{10}{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}}{30250 \, \sqrt{5 \, x + 3}} + \frac{2 \, \sqrt{10} \sqrt{5 \, x + 3}}{15125 \,{\left (\sqrt{2} \sqrt{-10 \, x + 5} - \sqrt{22}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/((5*x + 3)^(3/2)*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]