Optimal. Leaf size=81 \[ \frac{142}{6655 \sqrt{1-2 x}}-\frac{1231}{3630 \sqrt{1-2 x} (5 x+3)}+\frac{49}{66 (1-2 x)^{3/2} (5 x+3)}-\frac{142 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{1331 \sqrt{55}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.111732, antiderivative size = 81, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ \frac{142}{6655 \sqrt{1-2 x}}-\frac{1231}{3630 \sqrt{1-2 x} (5 x+3)}+\frac{49}{66 (1-2 x)^{3/2} (5 x+3)}-\frac{142 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{1331 \sqrt{55}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 9.71349, size = 65, normalized size = 0.8 \[ - \frac{142 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{73205} + \frac{142}{6655 \sqrt{- 2 x + 1}} + \frac{1231}{9075 \left (- 2 x + 1\right )^{\frac{3}{2}}} - \frac{1}{275 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**2/(1-2*x)**(5/2)/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.112496, size = 58, normalized size = 0.72 \[ \frac{-\frac{55 \left (852 x^2-2623 x-1866\right )}{(1-2 x)^{3/2} (5 x+3)}-426 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{219615} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^2/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.02, size = 54, normalized size = 0.7 \[{\frac{49}{363} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}+{\frac{28}{1331}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{2}{6655}\sqrt{1-2\,x} \left ( -{\frac{6}{5}}-2\,x \right ) ^{-1}}-{\frac{142\,\sqrt{55}}{73205}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^2/(1-2*x)^(5/2)/(3+5*x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.49302, size = 100, normalized size = 1.23 \[ \frac{71}{73205} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) + \frac{2 \,{\left (213 \,{\left (2 \, x - 1\right )}^{2} - 1771 \, x - 2079\right )}}{3993 \,{\left (5 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 11 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^2/((5*x + 3)^2*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.220206, size = 111, normalized size = 1.37 \[ \frac{\sqrt{55}{\left (213 \,{\left (10 \, x^{2} + x - 3\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{55}{\left (5 \, x - 8\right )} + 55 \, \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + \sqrt{55}{\left (852 \, x^{2} - 2623 \, x - 1866\right )}\right )}}{219615 \,{\left (10 \, x^{2} + x - 3\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^2/((5*x + 3)^2*(-2*x + 1)^(5/2)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**2/(1-2*x)**(5/2)/(3+5*x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.221482, size = 104, normalized size = 1.28 \[ \frac{71}{73205} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{7 \,{\left (24 \, x - 89\right )}}{3993 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} - \frac{\sqrt{-2 \, x + 1}}{1331 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^2/((5*x + 3)^2*(-2*x + 1)^(5/2)),x, algorithm="giac")
[Out]