Optimal. Leaf size=76 \[ -\frac{6561 x^5}{200}-\frac{408969 x^4}{1600}-\frac{124416 x^3}{125}-\frac{110180817 x^2}{40000}-\frac{2941619571 x}{400000}-\frac{188591347}{30976 (1-2 x)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (1-2 x)}{340736}+\frac{\log (5 x+3)}{20796875} \]
[Out]
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Rubi [A] time = 0.0906294, antiderivative size = 76, 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 \[ -\frac{6561 x^5}{200}-\frac{408969 x^4}{1600}-\frac{124416 x^3}{125}-\frac{110180817 x^2}{40000}-\frac{2941619571 x}{400000}-\frac{188591347}{30976 (1-2 x)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (1-2 x)}{340736}+\frac{\log (5 x+3)}{20796875} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{6561 x^{5}}{200} - \frac{408969 x^{4}}{1600} - \frac{124416 x^{3}}{125} - \frac{2644396573 \log{\left (- 2 x + 1 \right )}}{340736} + \frac{\log{\left (5 x + 3 \right )}}{20796875} + \int \left (- \frac{2941619571}{400000}\right )\, dx - \frac{110180817 \int x\, dx}{20000} - \frac{188591347}{30976 \left (- 2 x + 1\right )} + \frac{5764801}{5632 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**8/(1-2*x)**3/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0768206, size = 98, normalized size = 1.29 \[ -\frac{27}{200} (3 x+2)^5-\frac{2889 (3 x+2)^4}{1600}-\frac{17019 (3 x+2)^3}{1000}-\frac{5992353 (3 x+2)^2}{40000}-\frac{631722537 (3 x+2)}{400000}+\frac{188591347}{30976 (2 x-1)}+\frac{5764801}{5632 (1-2 x)^2}-\frac{2644396573 \log (3-6 x)}{340736}+\frac{\log (-3 (5 x+3))}{20796875} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)),x]
[Out]
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Maple [A] time = 0.013, size = 59, normalized size = 0.8 \[ -{\frac{6561\,{x}^{5}}{200}}-{\frac{408969\,{x}^{4}}{1600}}-{\frac{124416\,{x}^{3}}{125}}-{\frac{110180817\,{x}^{2}}{40000}}-{\frac{2941619571\,x}{400000}}+{\frac{\ln \left ( 3+5\,x \right ) }{20796875}}+{\frac{5764801}{5632\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{188591347}{-30976+61952\,x}}-{\frac{2644396573\,\ln \left ( -1+2\,x \right ) }{340736}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^8/(1-2*x)^3/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34522, size = 80, normalized size = 1.05 \[ -\frac{6561}{200} \, x^{5} - \frac{408969}{1600} \, x^{4} - \frac{124416}{125} \, x^{3} - \frac{110180817}{40000} \, x^{2} - \frac{2941619571}{400000} \, x + \frac{823543 \,{\left (916 \, x - 381\right )}}{61952 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{20796875} \, \log \left (5 \, x + 3\right ) - \frac{2644396573}{340736} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21844, size = 115, normalized size = 1.51 \[ -\frac{1397230560000 \, x^{7} + 9489524220000 \, x^{6} + 31855563036000 \, x^{5} + 77649212460600 \, x^{4} + 206501370522480 \, x^{3} - 283893518434680 \, x^{2} - 512 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (5 \, x + 3\right ) + 82637392906250 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 51350638082480 \, x + 53929198640625}{10648000000 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.461692, size = 65, normalized size = 0.86 \[ - \frac{6561 x^{5}}{200} - \frac{408969 x^{4}}{1600} - \frac{124416 x^{3}}{125} - \frac{110180817 x^{2}}{40000} - \frac{2941619571 x}{400000} + \frac{754365388 x - 313769883}{247808 x^{2} - 247808 x + 61952} - \frac{2644396573 \log{\left (x - \frac{1}{2} \right )}}{340736} + \frac{\log{\left (x + \frac{3}{5} \right )}}{20796875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**8/(1-2*x)**3/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.216893, size = 76, normalized size = 1. \[ -\frac{6561}{200} \, x^{5} - \frac{408969}{1600} \, x^{4} - \frac{124416}{125} \, x^{3} - \frac{110180817}{40000} \, x^{2} - \frac{2941619571}{400000} \, x + \frac{823543 \,{\left (916 \, x - 381\right )}}{61952 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{20796875} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) - \frac{2644396573}{340736} \,{\rm ln}\left ({\left | 2 \, x - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)*(2*x - 1)^3),x, algorithm="giac")
[Out]