Optimal. Leaf size=108 \[ -\frac{635 \sqrt{1-2 x}}{8232 (3 x+2)}-\frac{635 \sqrt{1-2 x}}{3528 (3 x+2)^2}+\frac{13 \sqrt{1-2 x}}{252 (3 x+2)^3}-\frac{\sqrt{1-2 x}}{252 (3 x+2)^4}-\frac{635 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{4116 \sqrt{21}} \]
[Out]
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Rubi [A] time = 0.131988, antiderivative size = 108, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ -\frac{635 \sqrt{1-2 x}}{8232 (3 x+2)}-\frac{635 \sqrt{1-2 x}}{3528 (3 x+2)^2}+\frac{13 \sqrt{1-2 x}}{252 (3 x+2)^3}-\frac{\sqrt{1-2 x}}{252 (3 x+2)^4}-\frac{635 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{4116 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]
[Out]
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Rubi in Sympy [A] time = 11.7493, size = 94, normalized size = 0.87 \[ - \frac{635 \sqrt{- 2 x + 1}}{8232 \left (3 x + 2\right )} - \frac{635 \sqrt{- 2 x + 1}}{3528 \left (3 x + 2\right )^{2}} + \frac{13 \sqrt{- 2 x + 1}}{252 \left (3 x + 2\right )^{3}} - \frac{\sqrt{- 2 x + 1}}{252 \left (3 x + 2\right )^{4}} - \frac{635 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{86436} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(2+3*x)**5/(1-2*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.126633, size = 63, normalized size = 0.58 \[ -\frac{\sqrt{1-2 x} \left (17145 x^3+47625 x^2+39366 x+10190\right )}{8232 (3 x+2)^4}-\frac{635 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{4116 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/(Sqrt[1 - 2*x]*(2 + 3*x)^5),x]
[Out]
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Maple [A] time = 0.017, size = 66, normalized size = 0.6 \[ 648\,{\frac{1}{ \left ( -4-6\,x \right ) ^{4}} \left ({\frac{635\, \left ( 1-2\,x \right ) ^{7/2}}{98784}}-{\frac{6985\, \left ( 1-2\,x \right ) ^{5/2}}{127008}}+{\frac{2717\, \left ( 1-2\,x \right ) ^{3/2}}{18144}}-{\frac{7171\,\sqrt{1-2\,x}}{54432}} \right ) }-{\frac{635\,\sqrt{21}}{86436}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(2+3*x)^5/(1-2*x)^(1/2),x)
[Out]
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Maxima [A] time = 1.50669, size = 149, normalized size = 1.38 \[ \frac{635}{172872} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{17145 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 146685 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 399399 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 351379 \, \sqrt{-2 \, x + 1}}{4116 \,{\left (81 \,{\left (2 \, x - 1\right )}^{4} + 756 \,{\left (2 \, x - 1\right )}^{3} + 2646 \,{\left (2 \, x - 1\right )}^{2} + 8232 \, x - 1715\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^5*sqrt(-2*x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.232563, size = 140, normalized size = 1.3 \[ -\frac{\sqrt{21}{\left (\sqrt{21}{\left (17145 \, x^{3} + 47625 \, x^{2} + 39366 \, x + 10190\right )} \sqrt{-2 \, x + 1} - 635 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{172872 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^5*sqrt(-2*x + 1)),x, algorithm="fricas")
[Out]
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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/(2+3*x)**5/(1-2*x)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.230436, size = 135, normalized size = 1.25 \[ \frac{635}{172872} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{17145 \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + 146685 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 399399 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 351379 \, \sqrt{-2 \, x + 1}}{65856 \,{\left (3 \, x + 2\right )}^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^5*sqrt(-2*x + 1)),x, algorithm="giac")
[Out]