Optimal. Leaf size=108 \[ -\frac{905 \sqrt{1-2 x}}{2058 (3 x+2)}-\frac{905 \sqrt{1-2 x}}{882 (3 x+2)^2}-\frac{467 \sqrt{1-2 x}}{126 (3 x+2)^3}+\frac{121}{14 \sqrt{1-2 x} (3 x+2)^3}-\frac{905 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{1029 \sqrt{21}} \]
[Out]
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Rubi [A] time = 0.136938, 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 \[ -\frac{905 \sqrt{1-2 x}}{2058 (3 x+2)}-\frac{905 \sqrt{1-2 x}}{882 (3 x+2)^2}-\frac{467 \sqrt{1-2 x}}{126 (3 x+2)^3}+\frac{121}{14 \sqrt{1-2 x} (3 x+2)^3}-\frac{905 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{1029 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]
[Out]
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Rubi in Sympy [A] time = 11.7242, size = 95, normalized size = 0.88 \[ - \frac{905 \sqrt{- 2 x + 1}}{2058 \left (3 x + 2\right )} - \frac{905 \sqrt{- 2 x + 1}}{882 \left (3 x + 2\right )^{2}} - \frac{467 \sqrt{- 2 x + 1}}{126 \left (3 x + 2\right )^{3}} - \frac{905 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{21609} + \frac{121}{14 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**(3/2)/(2+3*x)**4,x)
[Out]
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Mathematica [A] time = 0.159688, size = 63, normalized size = 0.58 \[ \frac{\frac{21 \left (16290 x^3+26245 x^2+13747 x+2316\right )}{\sqrt{1-2 x} (3 x+2)^3}-1810 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{43218} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)^(3/2)*(2 + 3*x)^4),x]
[Out]
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Maple [A] time = 0.02, size = 66, normalized size = 0.6 \[{\frac{484}{2401}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{108}{2401\, \left ( -4-6\,x \right ) ^{3}} \left ({\frac{1979}{36} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}}-{\frac{20083}{81} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}+{\frac{90601}{324}\sqrt{1-2\,x}} \right ) }-{\frac{905\,\sqrt{21}}{21609}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^(3/2)/(2+3*x)^4,x)
[Out]
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Maxima [A] time = 1.50706, size = 136, normalized size = 1.26 \[ \frac{905}{43218} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{8145 \,{\left (2 \, x - 1\right )}^{3} + 50680 \,{\left (2 \, x - 1\right )}^{2} + 208838 \, x - 33271}{1029 \,{\left (27 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 189 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 441 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 343 \, \sqrt{-2 \, x + 1}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*(-2*x + 1)^(3/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.226696, size = 136, normalized size = 1.26 \[ \frac{\sqrt{21}{\left (905 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right ) + \sqrt{21}{\left (16290 \, x^{3} + 26245 \, x^{2} + 13747 \, x + 2316\right )}\right )}}{43218 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*(-2*x + 1)^(3/2)),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/(1-2*x)**(3/2)/(2+3*x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.228173, size = 126, normalized size = 1.17 \[ \frac{905}{43218} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{484}{2401 \, \sqrt{-2 \, x + 1}} - \frac{17811 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 80332 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 90601 \, \sqrt{-2 \, x + 1}}{57624 \,{\left (3 \, x + 2\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*(-2*x + 1)^(3/2)),x, algorithm="giac")
[Out]