Optimal. Leaf size=108 \[ -\frac{95 \sqrt{1-2 x}}{8232 (3 x+2)}-\frac{95 \sqrt{1-2 x}}{3528 (3 x+2)^2}-\frac{19 \sqrt{1-2 x}}{252 (3 x+2)^3}+\frac{\sqrt{1-2 x}}{84 (3 x+2)^4}-\frac{95 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{4116 \sqrt{21}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.110913, antiderivative size = 108, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 4, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182 \[ -\frac{95 \sqrt{1-2 x}}{8232 (3 x+2)}-\frac{95 \sqrt{1-2 x}}{3528 (3 x+2)^2}-\frac{19 \sqrt{1-2 x}}{252 (3 x+2)^3}+\frac{\sqrt{1-2 x}}{84 (3 x+2)^4}-\frac{95 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{4116 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 10.5144, size = 94, normalized size = 0.87 \[ - \frac{95 \sqrt{- 2 x + 1}}{8232 \left (3 x + 2\right )} - \frac{95 \sqrt{- 2 x + 1}}{3528 \left (3 x + 2\right )^{2}} - \frac{19 \sqrt{- 2 x + 1}}{252 \left (3 x + 2\right )^{3}} + \frac{\sqrt{- 2 x + 1}}{84 \left (3 x + 2\right )^{4}} - \frac{95 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{86436} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)/(2+3*x)**5/(1-2*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.114459, size = 63, normalized size = 0.58 \[ -\frac{\sqrt{1-2 x} \left (2565 x^3+7125 x^2+7942 x+2790\right )}{8232 (3 x+2)^4}-\frac{95 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{4116 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.014, size = 66, normalized size = 0.6 \[ -1296\,{\frac{1}{ \left ( -4-6\,x \right ) ^{4}} \left ( -{\frac{95\, \left ( 1-2\,x \right ) ^{7/2}}{197568}}+{\frac{1045\, \left ( 1-2\,x \right ) ^{5/2}}{254016}}-{\frac{1387\, \left ( 1-2\,x \right ) ^{3/2}}{108864}}+{\frac{1447\,\sqrt{1-2\,x}}{108864}} \right ) }-{\frac{95\,\sqrt{21}}{86436}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)/(2+3*x)^5/(1-2*x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.50773, size = 149, normalized size = 1.38 \[ \frac{95}{172872} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{2565 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 21945 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 67963 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 70903 \, \sqrt{-2 \, x + 1}}{4116 \,{\left (81 \,{\left (2 \, x - 1\right )}^{4} + 756 \,{\left (2 \, x - 1\right )}^{3} + 2646 \,{\left (2 \, x - 1\right )}^{2} + 8232 \, x - 1715\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^5*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.238846, size = 140, normalized size = 1.3 \[ -\frac{\sqrt{21}{\left (\sqrt{21}{\left (2565 \, x^{3} + 7125 \, x^{2} + 7942 \, x + 2790\right )} \sqrt{-2 \, x + 1} - 95 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{172872 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^5*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)**5/(1-2*x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.21318, size = 135, normalized size = 1.25 \[ \frac{95}{172872} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{2565 \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + 21945 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 67963 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 70903 \, \sqrt{-2 \, x + 1}}{65856 \,{\left (3 \, x + 2\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)/((3*x + 2)^5*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]