Optimal. Leaf size=80 \[ \frac{11 (5 x+3)^2}{21 (1-2 x)^{3/2} (3 x+2)}-\frac{10 (1450 x+969)}{1029 \sqrt{1-2 x} (3 x+2)}-\frac{200 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{1029 \sqrt{21}} \]
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Rubi [A] time = 0.119727, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{11 (5 x+3)^2}{21 (1-2 x)^{3/2} (3 x+2)}-\frac{10 (1450 x+969)}{1029 \sqrt{1-2 x} (3 x+2)}-\frac{200 \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{1029 \sqrt{21}} \]
Antiderivative was successfully verified.
[In] Int[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 12.9208, size = 68, normalized size = 0.85 \[ - \frac{200 \sqrt{21} \operatorname{atanh}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}}{21609} - \frac{43500 x + 29070}{3087 \sqrt{- 2 x + 1} \left (3 x + 2\right )} + \frac{11 \left (5 x + 3\right )^{2}}{21 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (3 x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((3+5*x)**3/(1-2*x)**(5/2)/(2+3*x)**2,x)
[Out]
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Mathematica [A] time = 0.125909, size = 58, normalized size = 0.72 \[ \frac{\frac{21 \left (42475 x^2+21050 x-4839\right )}{(1-2 x)^{3/2} (3 x+2)}-200 \sqrt{21} \tanh ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )}{21609} \]
Antiderivative was successfully verified.
[In] Integrate[(3 + 5*x)^3/((1 - 2*x)^(5/2)*(2 + 3*x)^2),x]
[Out]
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Maple [A] time = 0.022, size = 54, normalized size = 0.7 \[{\frac{1331}{294} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}-{\frac{4719}{686}{\frac{1}{\sqrt{1-2\,x}}}}-{\frac{2}{3087}\sqrt{1-2\,x} \left ( -{\frac{4}{3}}-2\,x \right ) ^{-1}}-{\frac{200\,\sqrt{21}}{21609}{\it Artanh} \left ({\frac{\sqrt{21}}{7}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((3+5*x)^3/(1-2*x)^(5/2)/(2+3*x)^2,x)
[Out]
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Maxima [A] time = 1.49368, size = 100, normalized size = 1.25 \[ \frac{100}{21609} \, \sqrt{21} \log \left (-\frac{\sqrt{21} - 3 \, \sqrt{-2 \, x + 1}}{\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}}\right ) - \frac{42475 \,{\left (2 \, x - 1\right )}^{2} + 254100 \, x - 61831}{2058 \,{\left (3 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 7 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^2*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215973, size = 112, normalized size = 1.4 \[ \frac{\sqrt{21}{\left (100 \,{\left (6 \, x^{2} + x - 2\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{21}{\left (3 \, x - 5\right )} + 21 \, \sqrt{-2 \, x + 1}}{3 \, x + 2}\right ) - \sqrt{21}{\left (42475 \, x^{2} + 21050 \, x - 4839\right )}\right )}}{21609 \,{\left (6 \, x^{2} + x - 2\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^2*(-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((3+5*x)**3/(1-2*x)**(5/2)/(2+3*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.219024, size = 104, normalized size = 1.3 \[ \frac{100}{21609} \, \sqrt{21}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{21} + 6 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{21} + 3 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{121 \,{\left (117 \, x - 20\right )}}{1029 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} + \frac{\sqrt{-2 \, x + 1}}{1029 \,{\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3/((3*x + 2)^2*(-2*x + 1)^(5/2)),x, algorithm="giac")
[Out]