Optimal. Leaf size=135 \[ \frac{55 (1-2 x)^{3/2} (5 x+3)^3}{9 (3 x+2)}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{6 (3 x+2)^2}-\frac{220}{21} (1-2 x)^{3/2} (5 x+3)^2+\frac{55 (1-2 x)^{3/2} (603 x+209)}{1134}-\frac{935}{81} \sqrt{1-2 x}+\frac{935}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right ) \]
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Rubi [A] time = 0.230923, antiderivative size = 135, normalized size of antiderivative = 1., number of steps used = 8, number of rules used = 8, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{55 (1-2 x)^{3/2} (5 x+3)^3}{9 (3 x+2)}-\frac{(1-2 x)^{5/2} (5 x+3)^3}{6 (3 x+2)^2}-\frac{220}{21} (1-2 x)^{3/2} (5 x+3)^2+\frac{55 (1-2 x)^{3/2} (603 x+209)}{1134}-\frac{935}{81} \sqrt{1-2 x}+\frac{935}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^3,x]
[Out]
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Rubi in Sympy [A] time = 20.4617, size = 110, normalized size = 0.81 \[ \frac{11 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (7875 x + 2835\right )}{7938} - \frac{55 \left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{2}}{63 \left (3 x + 2\right )} - \frac{\left (- 2 x + 1\right )^{\frac{5}{2}} \left (5 x + 3\right )^{3}}{6 \left (3 x + 2\right )^{2}} - \frac{935 \left (- 2 x + 1\right )^{\frac{3}{2}}}{567} - \frac{935 \sqrt{- 2 x + 1}}{81} + \frac{935 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{243} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**(5/2)*(3+5*x)**3/(2+3*x)**3,x)
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Mathematica [A] time = 0.12804, size = 75, normalized size = 0.56 \[ \frac{\sqrt{1-2 x} \left (54000 x^5-24120 x^4-17460 x^3-67962 x^2-152833 x-64943\right )}{1134 (3 x+2)^2}+\frac{935}{81} \sqrt{\frac{7}{3}} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right ) \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^(5/2)*(3 + 5*x)^3)/(2 + 3*x)^3,x]
[Out]
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Maple [A] time = 0.016, size = 84, normalized size = 0.6 \[ -{\frac{125}{189} \left ( 1-2\,x \right ) ^{{\frac{7}{2}}}}-{\frac{10}{27} \left ( 1-2\,x \right ) ^{{\frac{5}{2}}}}-{\frac{370}{243} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{8198}{729}\sqrt{1-2\,x}}-{\frac{14}{81\, \left ( -4-6\,x \right ) ^{2}} \left ( -{\frac{73}{2} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}+{\frac{1519}{18}\sqrt{1-2\,x}} \right ) }+{\frac{935\,\sqrt{21}}{243}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3,x)
[Out]
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Maxima [A] time = 1.50288, size = 149, normalized size = 1.1 \[ -\frac{125}{189} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{10}{27} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{370}{243} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{935}{486} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{8198}{729} \, \sqrt{-2 \, x + 1} + \frac{7 \,{\left (657 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 1519 \, \sqrt{-2 \, x + 1}\right )}}{729 \,{\left (9 \,{\left (2 \, x - 1\right )}^{2} + 84 \, x + 7\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(5/2)/(3*x + 2)^3,x, algorithm="maxima")
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Fricas [A] time = 0.214413, size = 135, normalized size = 1. \[ \frac{\sqrt{3}{\left (6545 \, \sqrt{7}{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (\frac{\sqrt{3}{\left (3 \, x - 5\right )} - 3 \, \sqrt{7} \sqrt{-2 \, x + 1}}{3 \, x + 2}\right ) + \sqrt{3}{\left (54000 \, x^{5} - 24120 \, x^{4} - 17460 \, x^{3} - 67962 \, x^{2} - 152833 \, x - 64943\right )} \sqrt{-2 \, x + 1}\right )}}{3402 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(5/2)/(3*x + 2)^3,x, algorithm="fricas")
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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)*(3+5*x)**3/(2+3*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.21632, size = 159, normalized size = 1.18 \[ \frac{125}{189} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{10}{27} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{370}{243} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{935}{486} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{8198}{729} \, \sqrt{-2 \, x + 1} + \frac{7 \,{\left (657 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 1519 \, \sqrt{-2 \, x + 1}\right )}}{2916 \,{\left (3 \, x + 2\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(-2*x + 1)^(5/2)/(3*x + 2)^3,x, algorithm="giac")
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