Optimal. Leaf size=128 \[ -\frac{1415 \sqrt{1-2 x}}{4802 (3 x+2)}-\frac{1415 \sqrt{1-2 x}}{2058 (3 x+2)^2}+\frac{566}{441 \sqrt{1-2 x} (3 x+2)^2}-\frac{1091}{882 \sqrt{1-2 x} (3 x+2)^3}+\frac{121}{42 (1-2 x)^{3/2} (3 x+2)^3}-\frac{1415 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{2401 \sqrt{21}} \]
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Rubi [A] time = 0.159669, antiderivative size = 128, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ -\frac{1415 \sqrt{1-2 x}}{4802 (3 x+2)}-\frac{1415 \sqrt{1-2 x}}{2058 (3 x+2)^2}+\frac{566}{441 \sqrt{1-2 x} (3 x+2)^2}-\frac{1091}{882 \sqrt{1-2 x} (3 x+2)^3}+\frac{121}{42 (1-2 x)^{3/2} (3 x+2)^3}-\frac{1415 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{2401 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]
[Out]
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Rubi in Sympy [A] time = 14.3617, size = 114, normalized size = 0.89 \[ - \frac{1415 \sqrt{- 2 x + 1}}{4802 \left (3 x + 2\right )} - \frac{1415 \sqrt{- 2 x + 1}}{2058 \left (3 x + 2\right )^{2}} - \frac{1415 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{50421} + \frac{566}{441 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{2}} - \frac{1091}{882 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{3}} + \frac{121}{42 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (3 x + 2\right )^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**2/(1-2*x)**(5/2)/(2+3*x)**4,x)
[Out]
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Mathematica [A] time = 0.161477, size = 68, normalized size = 0.53 \[ \frac{-\frac{7 \left (152820 x^4+169800 x^3-26319 x^2-83655 x-23872\right )}{(1-2 x)^{3/2} (3 x+2)^3}-2830 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{100842} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^2/((1 - 2*x)^(5/2)*(2 + 3*x)^4),x]
[Out]
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Maple [A] time = 0.022, size = 75, normalized size = 0.6 \[{\frac{484}{7203} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}+{\frac{2728}{16807}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{108}{16807\, \left ( -4-6\,x \right ) ^{3}} \left ({\frac{1721}{12} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}}-{\frac{17395}{27} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}+{\frac{78155}{108}\sqrt{1-2\,x}} \right ) }-{\frac{1415\,\sqrt{21}}{50421}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^2/(1-2*x)^(5/2)/(2+3*x)^4,x)
[Out]
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Maxima [A] time = 1.48803, size = 149, normalized size = 1.16 \[ \frac{1415}{100842} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{38205 \,{\left (2 \, x - 1\right )}^{4} + 237720 \,{\left (2 \, x - 1\right )}^{3} + 457611 \,{\left (2 \, x - 1\right )}^{2} + 375144 \, x - 353584}{7203 \,{\left (27 \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - 189 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + 441 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 343 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215118, size = 157, normalized size = 1.23 \[ \frac{\sqrt{21}{\left (4245 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right ) + \sqrt{21}{\left (152820 \, x^{4} + 169800 \, x^{3} - 26319 \, x^{2} - 83655 \, x - 23872\right )}\right )}}{302526 \,{\left (54 \, x^{4} + 81 \, x^{3} + 18 \, x^{2} - 20 \, x - 8\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*(-2*x + 1)^(5/2)),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)**(5/2)/(2+3*x)**4,x)
[Out]
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GIAC/XCAS [A] time = 0.213834, size = 128, normalized size = 1. \[ \frac{1415}{100842} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{38205 \,{\left (2 \, x - 1\right )}^{4} + 237720 \,{\left (2 \, x - 1\right )}^{3} + 457611 \,{\left (2 \, x - 1\right )}^{2} + 375144 \, x - 353584}{7203 \,{\left (3 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 7 \, \sqrt{-2 \, x + 1}\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^2/((3*x + 2)^4*(-2*x + 1)^(5/2)),x, algorithm="giac")
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