Optimal. Leaf size=69 \[ \frac{2916 x^7}{175}+\frac{4374 x^6}{125}+\frac{28917 x^5}{3125}-\frac{157599 x^4}{6250}-\frac{48771 x^3}{3125}+\frac{463086 x^2}{78125}+\frac{2777053 x}{390625}-\frac{121}{1953125 (5 x+3)}+\frac{2134 \log (5 x+3)}{1953125} \]
[Out]
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Rubi [A] time = 0.0818827, antiderivative size = 69, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ \frac{2916 x^7}{175}+\frac{4374 x^6}{125}+\frac{28917 x^5}{3125}-\frac{157599 x^4}{6250}-\frac{48771 x^3}{3125}+\frac{463086 x^2}{78125}+\frac{2777053 x}{390625}-\frac{121}{1953125 (5 x+3)}+\frac{2134 \log (5 x+3)}{1953125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{2916 x^{7}}{175} + \frac{4374 x^{6}}{125} + \frac{28917 x^{5}}{3125} - \frac{157599 x^{4}}{6250} - \frac{48771 x^{3}}{3125} + \frac{2134 \log{\left (5 x + 3 \right )}}{1953125} + \int \frac{2777053}{390625}\, dx + \frac{926172 \int x\, dx}{78125} - \frac{121}{1953125 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**2*(2+3*x)**6/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0553587, size = 66, normalized size = 0.96 \[ \frac{11390625000 x^8+30754687500 x^7+20677781250 x^6-13442034375 x^5-21011090625 x^4-2349191250 x^3+7291044250 x^2+3997343145 x+149380 (5 x+3) \log (6 (5 x+3))+648854027}{136718750 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^2*(2 + 3*x)^6)/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.01, size = 52, normalized size = 0.8 \[{\frac{2777053\,x}{390625}}+{\frac{463086\,{x}^{2}}{78125}}-{\frac{48771\,{x}^{3}}{3125}}-{\frac{157599\,{x}^{4}}{6250}}+{\frac{28917\,{x}^{5}}{3125}}+{\frac{4374\,{x}^{6}}{125}}+{\frac{2916\,{x}^{7}}{175}}-{\frac{121}{5859375+9765625\,x}}+{\frac{2134\,\ln \left ( 3+5\,x \right ) }{1953125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^2*(2+3*x)^6/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34238, size = 69, normalized size = 1. \[ \frac{2916}{175} \, x^{7} + \frac{4374}{125} \, x^{6} + \frac{28917}{3125} \, x^{5} - \frac{157599}{6250} \, x^{4} - \frac{48771}{3125} \, x^{3} + \frac{463086}{78125} \, x^{2} + \frac{2777053}{390625} \, x - \frac{121}{1953125 \,{\left (5 \, x + 3\right )}} + \frac{2134}{1953125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.216816, size = 84, normalized size = 1.22 \[ \frac{2278125000 \, x^{8} + 6150937500 \, x^{7} + 4135556250 \, x^{6} - 2688406875 \, x^{5} - 4202218125 \, x^{4} - 469838250 \, x^{3} + 1458208850 \, x^{2} + 29876 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 583181130 \, x - 1694}{27343750 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.252785, size = 61, normalized size = 0.88 \[ \frac{2916 x^{7}}{175} + \frac{4374 x^{6}}{125} + \frac{28917 x^{5}}{3125} - \frac{157599 x^{4}}{6250} - \frac{48771 x^{3}}{3125} + \frac{463086 x^{2}}{78125} + \frac{2777053 x}{390625} + \frac{2134 \log{\left (5 x + 3 \right )}}{1953125} - \frac{121}{9765625 x + 5859375} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**2*(2+3*x)**6/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.208191, size = 126, normalized size = 1.83 \[ -\frac{1}{136718750} \,{\left (5 \, x + 3\right )}^{7}{\left (\frac{306180}{5 \, x + 3} - \frac{404838}{{\left (5 \, x + 3\right )}^{2}} - \frac{2189565}{{\left (5 \, x + 3\right )}^{3}} - \frac{2888550}{{\left (5 \, x + 3\right )}^{4}} - \frac{2081520}{{\left (5 \, x + 3\right )}^{5}} - \frac{1088290}{{\left (5 \, x + 3\right )}^{6}} - 29160\right )} - \frac{121}{1953125 \,{\left (5 \, x + 3\right )}} - \frac{2134}{1953125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6*(2*x - 1)^2/(5*x + 3)^2,x, algorithm="giac")
[Out]