Optimal. Leaf size=147 \[ \frac{7 (3 x+2)^5}{33 (1-2 x)^{3/2} (5 x+3)^2}-\frac{73 (3 x+2)^4}{3630 \sqrt{1-2 x} (5 x+3)^2}-\frac{3269 (3 x+2)^3}{199650 \sqrt{1-2 x} (5 x+3)}-\frac{256172 (3 x+2)^2}{366025 \sqrt{1-2 x}}-\frac{21 \sqrt{1-2 x} (736875 x+2211616)}{3660250}-\frac{6937 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{1830125 \sqrt{55}} \]
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Rubi [A] time = 0.307643, antiderivative size = 147, 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 \[ \frac{7 (3 x+2)^5}{33 (1-2 x)^{3/2} (5 x+3)^2}-\frac{73 (3 x+2)^4}{3630 \sqrt{1-2 x} (5 x+3)^2}-\frac{3269 (3 x+2)^3}{199650 \sqrt{1-2 x} (5 x+3)}-\frac{256172 (3 x+2)^2}{366025 \sqrt{1-2 x}}-\frac{21 \sqrt{1-2 x} (736875 x+2211616)}{3660250}-\frac{6937 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{1830125 \sqrt{55}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 32.0532, size = 133, normalized size = 0.9 \[ - \frac{\sqrt{- 2 x + 1} \left (696346875 x + 2089977120\right )}{164711250} - \frac{6937 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{100656875} - \frac{73 \left (3 x + 2\right )^{4}}{3630 \sqrt{- 2 x + 1} \left (5 x + 3\right )^{2}} - \frac{3269 \left (3 x + 2\right )^{3}}{199650 \sqrt{- 2 x + 1} \left (5 x + 3\right )} - \frac{256172 \left (3 x + 2\right )^{2}}{366025 \sqrt{- 2 x + 1}} + \frac{7 \left (3 x + 2\right )^{5}}{33 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6/(1-2*x)**(5/2)/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.148009, size = 76, normalized size = 0.52 \[ \frac{-\frac{55 \sqrt{1-2 x} \left (533664450 x^5+5763576060 x^4-6510290070 x^3-9509366452 x^2+253794537 x+1463964312\right )}{\left (10 x^2+x-3\right )^2}-41622 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{603941250} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^6/((1 - 2*x)^(5/2)*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.023, size = 84, normalized size = 0.6 \[{\frac{243}{1000} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{26973}{5000}\sqrt{1-2\,x}}+{\frac{117649}{31944} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}-{\frac{1563051}{117128}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{2}{366025\, \left ( -6-10\,x \right ) ^{2}} \left ({\frac{407}{10} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{4499}{50}\sqrt{1-2\,x}} \right ) }-{\frac{6937\,\sqrt{55}}{100656875}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6/(1-2*x)^(5/2)/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.51909, size = 149, normalized size = 1.01 \[ \frac{243}{1000} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{6937}{201313750} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{26973}{5000} \, \sqrt{-2 \, x + 1} + \frac{73267966785 \,{\left (2 \, x - 1\right )}^{3} + 342600082649 \,{\left (2 \, x - 1\right )}^{2} + 887178503750 \, x - 345719990000}{219615000 \,{\left (25 \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - 110 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + 121 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6/((5*x + 3)^3*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221216, size = 150, normalized size = 1.02 \[ \frac{\sqrt{55}{\left (20811 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{55}{\left (5 \, x - 8\right )} + 55 \, \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + \sqrt{55}{\left (533664450 \, x^{5} + 5763576060 \, x^{4} - 6510290070 \, x^{3} - 9509366452 \, x^{2} + 253794537 \, x + 1463964312\right )}\right )}}{603941250 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6/((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)**6/(1-2*x)**(5/2)/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.217143, size = 144, normalized size = 0.98 \[ \frac{243}{1000} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{6937}{201313750} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{26973}{5000} \, \sqrt{-2 \, x + 1} - \frac{16807 \,{\left (279 \, x - 101\right )}}{175692 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} + \frac{185 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - 409 \, \sqrt{-2 \, x + 1}}{3327500 \,{\left (5 \, x + 3\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6/((5*x + 3)^3*(-2*x + 1)^(5/2)),x, algorithm="giac")
[Out]