Optimal. Leaf size=88 \[ -\frac{50 \sqrt{1-2 x}}{1029 (3 x+2)}-\frac{50 \sqrt{1-2 x}}{441 (3 x+2)^2}+\frac{\sqrt{1-2 x}}{63 (3 x+2)^3}-\frac{100 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{1029 \sqrt{21}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.090328, antiderivative size = 88, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 4, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{50 \sqrt{1-2 x}}{1029 (3 x+2)}-\frac{50 \sqrt{1-2 x}}{441 (3 x+2)^2}+\frac{\sqrt{1-2 x}}{63 (3 x+2)^3}-\frac{100 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{1029 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 8.72895, size = 75, normalized size = 0.85 \[ - \frac{50 \sqrt{- 2 x + 1}}{1029 \left (3 x + 2\right )} - \frac{50 \sqrt{- 2 x + 1}}{441 \left (3 x + 2\right )^{2}} + \frac{\sqrt{- 2 x + 1}}{63 \left (3 x + 2\right )^{3}} - \frac{100 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{21609} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(2+3*x)**4/(1-2*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0976841, size = 58, normalized size = 0.66 \[ \frac{-\frac{21 \sqrt{1-2 x} \left (450 x^2+950 x+417\right )}{(3 x+2)^3}-100 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{21609} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^4),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 57, normalized size = 0.7 \[ 216\,{\frac{1}{ \left ( -4-6\,x \right ) ^{3}} \left ({\frac{25\, \left ( 1-2\,x \right ) ^{5/2}}{6174}}-{\frac{100\, \left ( 1-2\,x \right ) ^{3/2}}{3969}}+{\frac{41\,\sqrt{1-2\,x}}{1134}} \right ) }-{\frac{100\,\sqrt{21}}{21609}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(2+3*x)^4/(1-2*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.49497, size = 124, normalized size = 1.41 \[ \frac{50}{21609} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{4 \,{\left (225 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 1400 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 2009 \, \sqrt{-2 \, x + 1}\right )}}{1029 \,{\left (27 \,{\left (2 \, x - 1\right )}^{3} + 189 \,{\left (2 \, x - 1\right )}^{2} + 882 \, x - 98\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^4*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.230433, size = 120, normalized size = 1.36 \[ -\frac{\sqrt{21}{\left (\sqrt{21}{\left (450 \, x^{2} + 950 \, x + 417\right )} \sqrt{-2 \, x + 1} - 50 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{21609 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^4*sqrt(-2*x + 1)),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((3+5*x)/(2+3*x)**4/(1-2*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.211222, size = 113, normalized size = 1.28 \[ \frac{50}{21609} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{225 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 1400 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 2009 \, \sqrt{-2 \, x + 1}}{2058 \,{\left (3 \, x + 2\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^4*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]