Optimal. Leaf size=124 \[ \frac{7 (1-2 x)^{3/2}}{3 (3 x+2) (5 x+3)^2}+\frac{7103 \sqrt{1-2 x}}{30 (5 x+3)}-\frac{1133 \sqrt{1-2 x}}{30 (5 x+3)^2}+1400 \sqrt{\frac{7}{3}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{7209}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
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Rubi [A] time = 0.256805, antiderivative size = 124, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 6, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{7 (1-2 x)^{3/2}}{3 (3 x+2) (5 x+3)^2}+\frac{7103 \sqrt{1-2 x}}{30 (5 x+3)}-\frac{1133 \sqrt{1-2 x}}{30 (5 x+3)^2}+1400 \sqrt{\frac{7}{3}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )-\frac{7209}{5} \sqrt{\frac{11}{5}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Int[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 27.1644, size = 107, normalized size = 0.86 \[ \frac{7 \left (- 2 x + 1\right )^{\frac{3}{2}}}{3 \left (3 x + 2\right ) \left (5 x + 3\right )^{2}} + \frac{7103 \sqrt{- 2 x + 1}}{30 \left (5 x + 3\right )} - \frac{1133 \sqrt{- 2 x + 1}}{30 \left (5 x + 3\right )^{2}} + \frac{1400 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{3} - \frac{7209 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{25} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)/(2+3*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.218613, size = 93, normalized size = 0.75 \[ \frac{1}{50} \left (\frac{5 \sqrt{1-2 x} \left (35515 x^2+43806 x+13474\right )}{(3 x+2) (5 x+3)^2}-14418 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )\right )+1400 \sqrt{\frac{7}{3}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(1 - 2*x)^(5/2)/((2 + 3*x)^2*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.019, size = 82, normalized size = 0.7 \[ -{\frac{98}{3}\sqrt{1-2\,x} \left ( -{\frac{4}{3}}-2\,x \right ) ^{-1}}+{\frac{1400\,\sqrt{21}}{3}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) }+550\,{\frac{1}{ \left ( -6-10\,x \right ) ^{2}} \left ( -{\frac{141\, \left ( 1-2\,x \right ) ^{3/2}}{50}}+{\frac{1529\,\sqrt{1-2\,x}}{250}} \right ) }-{\frac{7209\,\sqrt{55}}{25}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)/(2+3*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.60069, size = 173, normalized size = 1.4 \[ \frac{7209}{50} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{700}{3} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) + \frac{35515 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 158642 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + 177023 \, \sqrt{-2 \, x + 1}}{5 \,{\left (75 \,{\left (2 \, x - 1\right )}^{3} + 505 \,{\left (2 \, x - 1\right )}^{2} + 2266 \, x - 286\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(5/2)/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="maxima")
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Fricas [A] time = 0.243497, size = 213, normalized size = 1.72 \[ \frac{\sqrt{5} \sqrt{3}{\left (7209 \, \sqrt{11} \sqrt{3}{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (\frac{\sqrt{5}{\left (5 \, x - 8\right )} + 5 \, \sqrt{11} \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + 7000 \, \sqrt{7} \sqrt{5}{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )} \log \left (\frac{\sqrt{3}{\left (3 \, x - 5\right )} - 3 \, \sqrt{7} \sqrt{-2 \, x + 1}}{3 \, x + 2}\right ) + \sqrt{5} \sqrt{3}{\left (35515 \, x^{2} + 43806 \, x + 13474\right )} \sqrt{-2 \, x + 1}\right )}}{150 \,{\left (75 \, x^{3} + 140 \, x^{2} + 87 \, x + 18\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(5/2)/((5*x + 3)^3*(3*x + 2)^2),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)**(5/2)/(2+3*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.215712, size = 166, normalized size = 1.34 \[ \frac{7209}{50} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{700}{3} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{49 \, \sqrt{-2 \, x + 1}}{3 \, x + 2} - \frac{11 \,{\left (705 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 1529 \, \sqrt{-2 \, x + 1}\right )}}{20 \,{\left (5 \, x + 3\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-2*x + 1)^(5/2)/((5*x + 3)^3*(3*x + 2)^2),x, algorithm="giac")
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