Optimal. Leaf size=84 \[ \frac{7 \sqrt{5 x+3} (3 x+2)^2}{11 \sqrt{1-2 x}}+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (10380 x+25003)}{8800}-\frac{56421 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{800 \sqrt{10}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.119773, 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 \[ \frac{7 \sqrt{5 x+3} (3 x+2)^2}{11 \sqrt{1-2 x}}+\frac{3 \sqrt{1-2 x} \sqrt{5 x+3} (10380 x+25003)}{8800}-\frac{56421 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{800 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^3/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 12.2705, size = 76, normalized size = 0.9 \[ \frac{\sqrt{- 2 x + 1} \sqrt{5 x + 3} \left (7785 x + \frac{75009}{4}\right )}{2200} - \frac{56421 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{8000} + \frac{7 \left (3 x + 2\right )^{2} \sqrt{5 x + 3}}{11 \sqrt{- 2 x + 1}} \]
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)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0865199, size = 64, normalized size = 0.76 \[ \frac{620631 \sqrt{10-20 x} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )-10 \sqrt{5 x+3} \left (11880 x^2+51678 x-97409\right )}{88000 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^3/((1 - 2*x)^(3/2)*Sqrt[3 + 5*x]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.021, size = 106, normalized size = 1.3 \[ -{\frac{1}{-176000+352000\,x} \left ( 1241262\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x-237600\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-620631\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -1033560\,x\sqrt{-10\,{x}^{2}-x+3}+1948180\,\sqrt{-10\,{x}^{2}-x+3} \right ) \sqrt{3+5\,x}\sqrt{1-2\,x}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3/(1-2*x)^(3/2)/(3+5*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.50145, size = 88, normalized size = 1.05 \[ -\frac{56421}{16000} \, \sqrt{5} \sqrt{2} \arcsin \left (\frac{20}{11} \, x + \frac{1}{11}\right ) + \frac{27}{40} \, \sqrt{-10 \, x^{2} - x + 3} x + \frac{2619}{800} \, \sqrt{-10 \, x^{2} - x + 3} - \frac{343 \, \sqrt{-10 \, x^{2} - x + 3}}{44 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.230667, size = 100, normalized size = 1.19 \[ \frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (11880 \, x^{2} + 51678 \, x - 97409\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 620631 \,{\left (2 \, x - 1\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{176000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{3}}{\left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**3/(1-2*x)**(3/2)/(3+5*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.231089, size = 96, normalized size = 1.14 \[ -\frac{56421}{8000} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) + \frac{{\left (594 \,{\left (4 \, \sqrt{5}{\left (5 \, x + 3\right )} + 63 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} - 620695 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{220000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3/(sqrt(5*x + 3)*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]