Optimal. Leaf size=154 \[ -\frac{46555 \sqrt{1-2 x}}{42 (5 x+3)}+\frac{6949 \sqrt{1-2 x}}{63 (3 x+2) (5 x+3)}+\frac{133 \sqrt{1-2 x}}{18 (3 x+2)^2 (5 x+3)}+\frac{7 \sqrt{1-2 x}}{9 (3 x+2)^3 (5 x+3)}-\frac{321161 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{7 \sqrt{21}}+1350 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
[Out]
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Rubi [A] time = 0.331451, antiderivative size = 154, normalized size of antiderivative = 1., number of steps used = 9, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ -\frac{46555 \sqrt{1-2 x}}{42 (5 x+3)}+\frac{6949 \sqrt{1-2 x}}{63 (3 x+2) (5 x+3)}+\frac{133 \sqrt{1-2 x}}{18 (3 x+2)^2 (5 x+3)}+\frac{7 \sqrt{1-2 x}}{9 (3 x+2)^3 (5 x+3)}-\frac{321161 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{7 \sqrt{21}}+1350 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 35.2434, size = 133, normalized size = 0.86 \[ - \frac{9311 \sqrt{- 2 x + 1}}{14 \left (3 x + 2\right )} - \frac{2005 \sqrt{- 2 x + 1}}{18 \left (3 x + 2\right ) \left (5 x + 3\right )} + \frac{133 \sqrt{- 2 x + 1}}{18 \left (3 x + 2\right )^{2} \left (5 x + 3\right )} + \frac{7 \sqrt{- 2 x + 1}}{9 \left (3 x + 2\right )^{3} \left (5 x + 3\right )} - \frac{321161 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{147} + 1350 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(3/2)/(2+3*x)**4/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.15733, size = 95, normalized size = 0.62 \[ -\frac{\sqrt{1-2 x} \left (418995 x^3+824092 x^2+539819 x+117752\right )}{14 (3 x+2)^3 (5 x+3)}-\frac{321161 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{7 \sqrt{21}}+1350 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(3/2)/((2 + 3*x)^4*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.02, size = 91, normalized size = 0.6 \[ 108\,{\frac{1}{ \left ( -4-6\,x \right ) ^{3}} \left ({\frac{7001\, \left ( 1-2\,x \right ) ^{5/2}}{84}}-{\frac{10603\, \left ( 1-2\,x \right ) ^{3/2}}{27}}+{\frac{49973\,\sqrt{1-2\,x}}{108}} \right ) }-{\frac{321161\,\sqrt{21}}{147}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) }+110\,{\frac{\sqrt{1-2\,x}}{-6/5-2\,x}}+1350\,{\it Artanh} \left ( 1/11\,\sqrt{55}\sqrt{1-2\,x} \right ) \sqrt{55} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(3/2)/(2+3*x)^4/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.50663, size = 197, normalized size = 1.28 \[ -675 \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) + \frac{321161}{294} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{418995 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 2905169 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 6712629 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 5168471 \, \sqrt{-2 \, x + 1}}{7 \,{\left (135 \,{\left (2 \, x - 1\right )}^{4} + 1242 \,{\left (2 \, x - 1\right )}^{3} + 4284 \,{\left (2 \, x - 1\right )}^{2} + 13132 \, x - 2793\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(3/2)/((5*x + 3)^2*(3*x + 2)^4),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219039, size = 215, normalized size = 1.4 \[ \frac{\sqrt{21}{\left (9450 \, \sqrt{55} \sqrt{21}{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (\frac{5 \, x - \sqrt{55} \sqrt{-2 \, x + 1} - 8}{5 \, x + 3}\right ) - \sqrt{21}{\left (418995 \, x^{3} + 824092 \, x^{2} + 539819 \, x + 117752\right )} \sqrt{-2 \, x + 1} + 321161 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right )\right )}}{294 \,{\left (135 \, x^{4} + 351 \, x^{3} + 342 \, x^{2} + 148 \, x + 24\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(3/2)/((5*x + 3)^2*(3*x + 2)^4),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**(3/2)/(2+3*x)**4/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.213834, size = 188, normalized size = 1.22 \[ -675 \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{321161}{294} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{275 \, \sqrt{-2 \, x + 1}}{5 \, x + 3} - \frac{63009 \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - 296884 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 349811 \, \sqrt{-2 \, x + 1}}{56 \,{\left (3 \, x + 2\right )}^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(3/2)/((5*x + 3)^2*(3*x + 2)^4),x, algorithm="giac")
[Out]