Optimal. Leaf size=62 \[ -\frac{243 x^3}{40}-\frac{35721 x^2}{800}-\frac{102303 x}{500}-\frac{2739541}{7744 (1-2 x)}+\frac{117649}{1408 (1-2 x)^2}-\frac{12761315 \log (1-2 x)}{42592}+\frac{\log (5 x+3)}{831875} \]
[Out]
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Rubi [A] time = 0.0742473, antiderivative size = 62, 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 \[ -\frac{243 x^3}{40}-\frac{35721 x^2}{800}-\frac{102303 x}{500}-\frac{2739541}{7744 (1-2 x)}+\frac{117649}{1408 (1-2 x)^2}-\frac{12761315 \log (1-2 x)}{42592}+\frac{\log (5 x+3)}{831875} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{243 x^{3}}{40} - \frac{12761315 \log{\left (- 2 x + 1 \right )}}{42592} + \frac{\log{\left (5 x + 3 \right )}}{831875} + \int \left (- \frac{102303}{500}\right )\, dx - \frac{35721 \int x\, dx}{400} - \frac{2739541}{7744 \left (- 2 x + 1\right )} + \frac{117649}{1408 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**6/(1-2*x)**3/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0481654, size = 55, normalized size = 0.89 \[ \frac{-\frac{11 \left (235224000 x^5+1493672400 x^4+6252253920 x^3-3308307948 x^2-9050078692 x+3661042443\right )}{(1-2 x)^2}-31903287500 \log (5-10 x)+128 \log (5 x+3)}{106480000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^6/((1 - 2*x)^3*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.013, size = 49, normalized size = 0.8 \[ -{\frac{243\,{x}^{3}}{40}}-{\frac{35721\,{x}^{2}}{800}}-{\frac{102303\,x}{500}}+{\frac{\ln \left ( 3+5\,x \right ) }{831875}}+{\frac{117649}{1408\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{2739541}{-7744+15488\,x}}-{\frac{12761315\,\ln \left ( -1+2\,x \right ) }{42592}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^6/(1-2*x)^3/(3+5*x),x)
[Out]
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Maxima [A] time = 1.36166, size = 66, normalized size = 1.06 \[ -\frac{243}{40} \, x^{3} - \frac{35721}{800} \, x^{2} - \frac{102303}{500} \, x + \frac{16807 \,{\left (652 \, x - 249\right )}}{15488 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{831875} \, \log \left (5 \, x + 3\right ) - \frac{12761315}{42592} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212429, size = 101, normalized size = 1.63 \[ -\frac{2587464000 \, x^{5} + 16430396400 \, x^{4} + 68774793120 \, x^{3} - 82391322420 \, x^{2} - 128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 31903287500 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 53550930620 \, x + 28771483125}{106480000 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.439193, size = 51, normalized size = 0.82 \[ - \frac{243 x^{3}}{40} - \frac{35721 x^{2}}{800} - \frac{102303 x}{500} + \frac{10958164 x - 4184943}{61952 x^{2} - 61952 x + 15488} - \frac{12761315 \log{\left (x - \frac{1}{2} \right )}}{42592} + \frac{\log{\left (x + \frac{3}{5} \right )}}{831875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**6/(1-2*x)**3/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.209239, size = 62, normalized size = 1. \[ -\frac{243}{40} \, x^{3} - \frac{35721}{800} \, x^{2} - \frac{102303}{500} \, x + \frac{16807 \,{\left (652 \, x - 249\right )}}{15488 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{831875} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{12761315}{42592} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^6/((5*x + 3)*(2*x - 1)^3),x, algorithm="giac")
[Out]