Optimal. Leaf size=66 \[ -\frac{729 x^2}{400}-\frac{31347 x}{2000}-\frac{67228}{1331 (1-2 x)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (5 x+3)}{9150625} \]
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Rubi [A] time = 0.0757749, 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 \[ -\frac{729 x^2}{400}-\frac{31347 x}{2000}-\frac{67228}{1331 (1-2 x)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (5 x+3)}{9150625} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{7383075 \log{\left (- 2 x + 1 \right )}}{234256} + \frac{204 \log{\left (5 x + 3 \right )}}{9150625} + \int \left (- \frac{31347}{2000}\right )\, dx - \frac{729 \int x\, dx}{200} - \frac{1}{831875 \left (5 x + 3\right )} - \frac{67228}{1331 \left (- 2 x + 1\right )} + \frac{117649}{7744 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0742069, size = 74, normalized size = 1.12 \[ -\frac{729 (1-2 x)^2}{1600}+\frac{2187}{250} (1-2 x)+\frac{67228}{1331 (2 x-1)}-\frac{1}{831875 (5 x+3)}+\frac{117649}{7744 (1-2 x)^2}-\frac{7383075 \log (1-2 x)}{234256}+\frac{204 \log (10 x+6)}{9150625} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.014, size = 53, normalized size = 0.8 \[ -{\frac{729\,{x}^{2}}{400}}-{\frac{31347\,x}{2000}}-{\frac{1}{2495625+4159375\,x}}+{\frac{204\,\ln \left ( 3+5\,x \right ) }{9150625}}+{\frac{117649}{7744\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{67228}{-1331+2662\,x}}-{\frac{7383075\,\ln \left ( -1+2\,x \right ) }{234256}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6/(1-2*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.36592, size = 73, normalized size = 1.11 \[ -\frac{729}{400} \, x^{2} - \frac{31347}{2000} \, x + \frac{26891199744 \, x^{2} + 6733304631 \, x - 5640849439}{53240000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{204}{9150625} \, \log \left (5 \, x + 3\right ) - \frac{7383075}{234256} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212648, size = 122, normalized size = 1.85 \[ -\frac{21346578000 \, x^{5} + 175041939600 \, x^{4} - 80903530620 \, x^{3} - 356854410264 \, x^{2} - 13056 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 18457687500 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 46529265321 \, x + 62049343829}{585640000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.511198, size = 56, normalized size = 0.85 \[ - \frac{729 x^{2}}{400} - \frac{31347 x}{2000} + \frac{26891199744 x^{2} + 6733304631 x - 5640849439}{1064800000 x^{3} - 425920000 x^{2} - 372680000 x + 159720000} - \frac{7383075 \log{\left (x - \frac{1}{2} \right )}}{234256} + \frac{204 \log{\left (x + \frac{3}{5} \right )}}{9150625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.218881, size = 127, normalized size = 1.92 \[ -\frac{{\left (5 \, x + 3\right )}^{2}{\left (\frac{555011028}{5 \, x + 3} - \frac{13845990449}{{\left (5 \, x + 3\right )}^{2}} + \frac{50757096489}{{\left (5 \, x + 3\right )}^{3}} + 21346578\right )}}{73205000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{1}{831875 \,{\left (5 \, x + 3\right )}} + \frac{315171}{10000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{7383075}{234256} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="giac")
[Out]