Optimal. Leaf size=121 \[ -\frac{(1-2 x)^{5/2} (3 x+2)^3}{5 (5 x+3)}+\frac{11}{75} (1-2 x)^{5/2} (3 x+2)^2+\frac{188 (1-2 x)^{3/2}}{9375}-\frac{2 (1-2 x)^{5/2} (2850 x+6191)}{65625}+\frac{2068 \sqrt{1-2 x}}{15625}-\frac{2068 \sqrt{\frac{11}{5}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{15625} \]
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Rubi [A] time = 0.192115, antiderivative size = 121, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 6, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ -\frac{(1-2 x)^{5/2} (3 x+2)^3}{5 (5 x+3)}+\frac{11}{75} (1-2 x)^{5/2} (3 x+2)^2+\frac{188 (1-2 x)^{3/2}}{9375}-\frac{2 (1-2 x)^{5/2} (2850 x+6191)}{65625}+\frac{2068 \sqrt{1-2 x}}{15625}-\frac{2068 \sqrt{\frac{11}{5}} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{15625} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [A] time = 21.935, size = 102, normalized size = 0.84 \[ - \frac{\left (- 2 x + 1\right )^{\frac{5}{2}} \left (3 x + 2\right )^{3}}{5 \left (5 x + 3\right )} + \frac{11 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (3 x + 2\right )^{2}}{75} - \frac{\left (- 2 x + 1\right )^{\frac{5}{2}} \left (17100 x + 37146\right )}{196875} + \frac{188 \left (- 2 x + 1\right )^{\frac{3}{2}}}{9375} + \frac{2068 \sqrt{- 2 x + 1}}{15625} - \frac{2068 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{78125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)*(2+3*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.12092, size = 73, normalized size = 0.6 \[ \frac{\frac{5 \sqrt{1-2 x} \left (1575000 x^5+427500 x^4-1858950 x^3+152105 x^2+680930 x+16794\right )}{5 x+3}-43428 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{1640625} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^(5/2)*(2 + 3*x)^3)/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.016, size = 81, normalized size = 0.7 \[{\frac{3}{50} \left ( 1-2\,x \right ) ^{{\frac{9}{2}}}}-{\frac{351}{1750} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}}+{\frac{18}{3125} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}}+{\frac{194}{9375} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}+{\frac{418}{3125}\sqrt{1-2\,x}}+{\frac{242}{78125}\sqrt{1-2\,x} \left ( -{\frac{6}{5}}-2\,x \right ) ^{-1}}-{\frac{2068\,\sqrt{55}}{78125}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.53054, size = 132, normalized size = 1.09 \[ \frac{3}{50} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{351}{1750} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{18}{3125} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{194}{9375} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1034}{78125} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) + \frac{418}{3125} \, \sqrt{-2 \, x + 1} - \frac{121 \, \sqrt{-2 \, x + 1}}{15625 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(-2*x + 1)^(5/2)/(5*x + 3)^2,x, algorithm="maxima")
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Fricas [A] time = 0.212319, size = 122, normalized size = 1.01 \[ \frac{\sqrt{5}{\left (21714 \, \sqrt{11}{\left (5 \, x + 3\right )} \log \left (\frac{\sqrt{5}{\left (5 \, x - 8\right )} + 5 \, \sqrt{11} \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + \sqrt{5}{\left (1575000 \, x^{5} + 427500 \, x^{4} - 1858950 \, x^{3} + 152105 \, x^{2} + 680930 \, x + 16794\right )} \sqrt{-2 \, x + 1}\right )}}{1640625 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(-2*x + 1)^(5/2)/(5*x + 3)^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)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217818, size = 165, normalized size = 1.36 \[ \frac{3}{50} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{351}{1750} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{18}{3125} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{194}{9375} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{1034}{78125} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) + \frac{418}{3125} \, \sqrt{-2 \, x + 1} - \frac{121 \, \sqrt{-2 \, x + 1}}{15625 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^3*(-2*x + 1)^(5/2)/(5*x + 3)^2,x, algorithm="giac")
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