Optimal. Leaf size=66 \[ \frac{729 x^2}{1000}+\frac{2916 x}{625}+\frac{117649}{21296 (1-2 x)}-\frac{202}{4159375 (5 x+3)}-\frac{1}{756250 (5 x+3)^2}+\frac{1563051 \log (1-2 x)}{234256}+\frac{17139 \log (5 x+3)}{45753125} \]
[Out]
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Rubi [A] time = 0.0749327, antiderivative size = 66, 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 \[ \frac{729 x^2}{1000}+\frac{2916 x}{625}+\frac{117649}{21296 (1-2 x)}-\frac{202}{4159375 (5 x+3)}-\frac{1}{756250 (5 x+3)^2}+\frac{1563051 \log (1-2 x)}{234256}+\frac{17139 \log (5 x+3)}{45753125} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{1563051 \log{\left (- 2 x + 1 \right )}}{234256} + \frac{17139 \log{\left (5 x + 3 \right )}}{45753125} + \int \frac{2916}{625}\, dx + \frac{729 \int x\, dx}{500} - \frac{202}{4159375 \left (5 x + 3\right )} - \frac{1}{756250 \left (5 x + 3\right )^{2}} + \frac{117649}{21296 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.0861269, size = 60, normalized size = 0.91 \[ \frac{11 \left (97029900 x^2+620991360 x+\frac{735306250}{1-2 x}-\frac{6464}{5 x+3}-\frac{176}{(5 x+3)^2}-334753155\right )+9769068750 \log (1-2 x)+548448 \log (10 x+6)}{1464100000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^6/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.014, size = 53, normalized size = 0.8 \[{\frac{729\,{x}^{2}}{1000}}+{\frac{2916\,x}{625}}-{\frac{1}{756250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{202}{12478125+20796875\,x}}+{\frac{17139\,\ln \left ( 3+5\,x \right ) }{45753125}}-{\frac{117649}{-21296+42592\,x}}+{\frac{1563051\,\ln \left ( -1+2\,x \right ) }{234256}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6/(1-2*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.3442, size = 73, normalized size = 1.11 \[ \frac{729}{1000} \, x^{2} + \frac{2916}{625} \, x - \frac{9191360445 \, x^{2} + 11029597158 \, x + 3308868341}{66550000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{17139}{45753125} \, \log \left (5 \, x + 3\right ) + \frac{1563051}{234256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210386, size = 122, normalized size = 1.85 \[ \frac{26683222500 \, x^{5} + 189450879750 \, x^{4} + 113136863400 \, x^{3} - 146893374705 \, x^{2} + 274224 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 4884534375 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) - 152064641058 \, x - 36397551751}{732050000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.469936, size = 56, normalized size = 0.85 \[ \frac{729 x^{2}}{1000} + \frac{2916 x}{625} - \frac{9191360445 x^{2} + 11029597158 x + 3308868341}{3327500000 x^{3} + 2329250000 x^{2} - 798600000 x - 598950000} + \frac{1563051 \log{\left (x - \frac{1}{2} \right )}}{234256} + \frac{17139 \log{\left (x + \frac{3}{5} \right )}}{45753125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208401, size = 127, normalized size = 1.92 \[ \frac{{\left (2 \, x - 1\right )}^{2}{\left (\frac{25615893600}{2 \, x - 1} + \frac{93337977265}{{\left (2 \, x - 1\right )}^{2}} + \frac{95568773322}{{\left (2 \, x - 1\right )}^{3}} + 1334161125\right )}}{292820000 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} - \frac{117649}{21296 \,{\left (2 \, x - 1\right )}} - \frac{333639}{50000} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{17139}{45753125} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^6/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="giac")
[Out]