Optimal. Leaf size=154 \[ \frac{(5 x+3)^{5/2} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{33}{20} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^2+\frac{9748787 \sqrt{1-2 x} (5 x+3)^{3/2}}{51200}+\frac{9 \sqrt{1-2 x} (5 x+3)^{5/2} (13820 x+27937)}{6400}+\frac{321709971 \sqrt{1-2 x} \sqrt{5 x+3}}{204800}-\frac{3538809681 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{204800 \sqrt{10}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.223326, antiderivative size = 154, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231 \[ \frac{(5 x+3)^{5/2} (3 x+2)^3}{\sqrt{1-2 x}}+\frac{33}{20} \sqrt{1-2 x} (5 x+3)^{5/2} (3 x+2)^2+\frac{9748787 \sqrt{1-2 x} (5 x+3)^{3/2}}{51200}+\frac{9 \sqrt{1-2 x} (5 x+3)^{5/2} (13820 x+27937)}{6400}+\frac{321709971 \sqrt{1-2 x} \sqrt{5 x+3}}{204800}-\frac{3538809681 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{204800 \sqrt{10}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 23.5348, size = 143, normalized size = 0.93 \[ \frac{33 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{2} \left (5 x + 3\right )^{\frac{5}{2}}}{20} + \frac{\sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{5}{2}} \left (\frac{2332125 x}{2} + \frac{18857475}{8}\right )}{60000} + \frac{9748787 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{\frac{3}{2}}}{51200} + \frac{321709971 \sqrt{- 2 x + 1} \sqrt{5 x + 3}}{204800} - \frac{3538809681 \sqrt{10} \operatorname{asin}{\left (\frac{\sqrt{22} \sqrt{5 x + 3}}{11} \right )}}{2048000} + \frac{\left (3 x + 2\right )^{3} \left (5 x + 3\right )^{\frac{5}{2}}}{\sqrt{- 2 x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**3*(3+5*x)**(5/2)/(1-2*x)**(3/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.117105, size = 79, normalized size = 0.51 \[ \frac{3538809681 \sqrt{10-20 x} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )-10 \sqrt{5 x+3} \left (13824000 x^5+65836800 x^4+148751040 x^3+233394520 x^2+381820658 x-538018839\right )}{2048000 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)^3*(3 + 5*x)^(5/2))/(1 - 2*x)^(3/2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.019, size = 157, normalized size = 1. \[ -{\frac{1}{-4096000+8192000\,x} \left ( -276480000\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}-1316736000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}-2975020800\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+7077619362\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) x-4667890400\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}-3538809681\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -7636413160\,x\sqrt{-10\,{x}^{2}-x+3}+10760376780\,\sqrt{-10\,{x}^{2}-x+3} \right ) \sqrt{1-2\,x}\sqrt{3+5\,x}{\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.50941, size = 170, normalized size = 1.1 \[ -\frac{675 \, x^{6}}{2 \, \sqrt{-10 \, x^{2} - x + 3}} - \frac{57915 \, x^{5}}{32 \, \sqrt{-10 \, x^{2} - x + 3}} - \frac{588291 \, x^{4}}{128 \, \sqrt{-10 \, x^{2} - x + 3}} - \frac{40330643 \, x^{3}}{5120 \, \sqrt{-10 \, x^{2} - x + 3}} - \frac{52185737 \, x^{2}}{4096 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{3538809681}{4096000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) + \frac{1544632221 \, x}{204800 \, \sqrt{-10 \, x^{2} - x + 3}} + \frac{1614056517}{204800 \, \sqrt{-10 \, x^{2} - x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.244254, size = 120, normalized size = 0.78 \[ \frac{\sqrt{10}{\left (2 \, \sqrt{10}{\left (13824000 \, x^{5} + 65836800 \, x^{4} + 148751040 \, x^{3} + 233394520 \, x^{2} + 381820658 \, x - 538018839\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - 3538809681 \,{\left (2 \, x - 1\right )} \arctan \left (\frac{\sqrt{10}{\left (20 \, x + 1\right )}}{20 \, \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}\right )\right )}}{4096000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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)**3*(3+5*x)**(5/2)/(1-2*x)**(3/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.235076, size = 149, normalized size = 0.97 \[ -\frac{3538809681}{2048000} \, \sqrt{10} \arcsin \left (\frac{1}{11} \, \sqrt{22} \sqrt{5 \, x + 3}\right ) + \frac{{\left (2 \,{\left (4 \,{\left (24 \,{\left (36 \,{\left (16 \, \sqrt{5}{\left (5 \, x + 3\right )} + 141 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 42197 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 9748787 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} + 536183285 \, \sqrt{5}\right )}{\left (5 \, x + 3\right )} - 17694048405 \, \sqrt{5}\right )} \sqrt{5 \, x + 3} \sqrt{-10 \, x + 5}}{25600000 \,{\left (2 \, x - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^(5/2)*(3*x + 2)^3/(-2*x + 1)^(3/2),x, algorithm="giac")
[Out]