Optimal. Leaf size=127 \[ \frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} (5 x+3)^2}-\frac{73 (3 x+2)^3}{3630 \sqrt{1-2 x} (5 x+3)^2}-\frac{317 (3 x+2)^2}{19965 \sqrt{1-2 x} (5 x+3)}-\frac{3 (544568-333311 x)}{732050 \sqrt{1-2 x}}-\frac{4693 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{366025 \sqrt{55}} \]
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Rubi [A] time = 0.247256, antiderivative size = 127, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.208 \[ \frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} (5 x+3)^2}-\frac{73 (3 x+2)^3}{3630 \sqrt{1-2 x} (5 x+3)^2}-\frac{317 (3 x+2)^2}{19965 \sqrt{1-2 x} (5 x+3)}-\frac{3 (544568-333311 x)}{732050 \sqrt{1-2 x}}-\frac{4693 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{366025 \sqrt{55}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 25.1236, size = 114, normalized size = 0.9 \[ - \frac{- 14998995 x + 24505560}{10980750 \sqrt{- 2 x + 1}} - \frac{4693 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{20131375} - \frac{73 \left (3 x + 2\right )^{3}}{3630 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{2}} - \frac{317 \left (3 x + 2\right )^{2}}{19965 \sqrt{- 2 x + 1} \left (5 x + 3\right )} + \frac{7 \left (3 x + 2\right )^{4}}{33 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5/(1-2*x)**(5/2)/(3+5*x)**3,x)
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Mathematica [A] time = 0.124153, size = 71, normalized size = 0.56 \[ \frac{-\frac{55 \sqrt{1-2 x} \left (106732890 x^4-248761830 x^3-309826828 x^2-10907307 x+37428168\right )}{\left (10 x^2+x-3\right )^2}-28158 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{120788250} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.023, size = 75, normalized size = 0.6 \[ -{\frac{243}{500}\sqrt{1-2\,x}}+{\frac{16807}{15972} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}-{\frac{36015}{14641}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{4}{73205\, \left ( -6-10\,x \right ) ^{2}} \left ({\frac{341}{20} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{3773}{100}\sqrt{1-2\,x}} \right ) }-{\frac{4693\,\sqrt{55}}{20131375}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.51615, size = 136, normalized size = 1.07 \[ \frac{4693}{40262750} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{243}{500} \, \sqrt{-2 \, x + 1} + \frac{1350542040 \,{\left (2 \, x - 1\right )}^{3} + 6520170349 \,{\left (2 \, x - 1\right )}^{2} + 18157562500 \, x - 6282516625}{21961500 \,{\left (25 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 110 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 121 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^3*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.229432, size = 143, normalized size = 1.13 \[ \frac{\sqrt{55}{\left (14079 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{55}{\left (5 \, x - 8\right )} + 55 \, \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + \sqrt{55}{\left (106732890 \, x^{4} - 248761830 \, x^{3} - 309826828 \, x^{2} - 10907307 \, x + 37428168\right )}\right )}}{120788250 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^3*(-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((2+3*x)**5/(1-2*x)**(5/2)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.216835, size = 132, normalized size = 1.04 \[ \frac{4693}{40262750} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{243}{500} \, \sqrt{-2 \, x + 1} - \frac{2401 \,{\left (360 \, x - 103\right )}}{175692 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} + \frac{155 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 343 \, \sqrt{-2 \, x + 1}}{665500 \,{\left (5 \, x + 3\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^3*(-2*x + 1)^(5/2)),x, algorithm="giac")
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