Optimal. Leaf size=58 \[ -\frac{729 x^4}{200}-\frac{8019 x^3}{500}-\frac{335097 x^2}{10000}-\frac{2682909 x}{50000}-\frac{1}{171875 (5 x+3)}-\frac{117649 \log (1-2 x)}{3872}+\frac{8 \log (5 x+3)}{75625} \]
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Rubi [A] time = 0.0633682, antiderivative size = 58, 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 \[ -\frac{729 x^4}{200}-\frac{8019 x^3}{500}-\frac{335097 x^2}{10000}-\frac{2682909 x}{50000}-\frac{1}{171875 (5 x+3)}-\frac{117649 \log (1-2 x)}{3872}+\frac{8 \log (5 x+3)}{75625} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{729 x^{4}}{200} - \frac{8019 x^{3}}{500} - \frac{117649 \log{\left (- 2 x + 1 \right )}}{3872} + \frac{8 \log{\left (5 x + 3 \right )}}{75625} + \int \left (- \frac{2682909}{50000}\right )\, dx - \frac{335097 \int x\, dx}{5000} - \frac{1}{171875 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6/(1-2*x)/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0640142, size = 54, normalized size = 0.93 \[ \frac{-80190000 x^4-352836000 x^3-737213400 x^2-1180479960 x-\frac{128}{5 x+3}+823659705}{22000000}-\frac{117649 \log (1-2 x)}{3872}+\frac{8 \log (10 x+6)}{75625} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^6/((1 - 2*x)*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.013, size = 45, normalized size = 0.8 \[ -{\frac{729\,{x}^{4}}{200}}-{\frac{8019\,{x}^{3}}{500}}-{\frac{335097\,{x}^{2}}{10000}}-{\frac{2682909\,x}{50000}}-{\frac{1}{515625+859375\,x}}+{\frac{8\,\ln \left ( 3+5\,x \right ) }{75625}}-{\frac{117649\,\ln \left ( -1+2\,x \right ) }{3872}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6/(1-2*x)/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.35614, size = 59, normalized size = 1.02 \[ -\frac{729}{200} \, x^{4} - \frac{8019}{500} \, x^{3} - \frac{335097}{10000} \, x^{2} - \frac{2682909}{50000} \, x - \frac{1}{171875 \,{\left (5 \, x + 3\right )}} + \frac{8}{75625} \, \log \left (5 \, x + 3\right ) - \frac{117649}{3872} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)^2*(2*x - 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.210747, size = 81, normalized size = 1.4 \[ -\frac{1102612500 \, x^{5} + 5513062500 \, x^{4} + 13047581250 \, x^{3} + 22313610000 \, x^{2} - 6400 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 1838265625 \,{\left (5 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 9738959670 \, x + 352}{60500000 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)^2*(2*x - 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.373878, size = 51, normalized size = 0.88 \[ - \frac{729 x^{4}}{200} - \frac{8019 x^{3}}{500} - \frac{335097 x^{2}}{10000} - \frac{2682909 x}{50000} - \frac{117649 \log{\left (x - \frac{1}{2} \right )}}{3872} + \frac{8 \log{\left (x + \frac{3}{5} \right )}}{75625} - \frac{1}{859375 x + 515625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6/(1-2*x)/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.206319, size = 109, normalized size = 1.88 \[ -\frac{27}{250000} \,{\left (5 \, x + 3\right )}^{4}{\left (\frac{540}{5 \, x + 3} + \frac{4635}{{\left (5 \, x + 3\right )}^{2}} + \frac{51145}{{\left (5 \, x + 3\right )}^{3}} + 54\right )} - \frac{1}{171875 \,{\left (5 \, x + 3\right )}} + \frac{607689}{20000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{117649}{3872} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)^2*(2*x - 1)),x, algorithm="giac")
[Out]