Optimal. Leaf size=37 \[ -\frac{6 x^4}{5}+\frac{172 x^3}{75}-\frac{183 x^2}{125}-\frac{27 x}{625}+\frac{1331 \log (5 x+3)}{3125} \]
[Out]
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Rubi [A] time = 0.0363987, antiderivative size = 37, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{6 x^4}{5}+\frac{172 x^3}{75}-\frac{183 x^2}{125}-\frac{27 x}{625}+\frac{1331 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{6 x^{4}}{5} + \frac{172 x^{3}}{75} + \frac{1331 \log{\left (5 x + 3 \right )}}{3125} + \int \left (- \frac{27}{625}\right )\, dx - \frac{366 \int x\, dx}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0208827, size = 35, normalized size = 0.95 \[ \frac{3993 \log (5 x+3)-5 \left (2250 x^4-4300 x^3+2745 x^2+81 x-2160\right )}{9375} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x))/(3 + 5*x),x]
[Out]
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Maple [A] time = 0.004, size = 28, normalized size = 0.8 \[ -{\frac{27\,x}{625}}-{\frac{183\,{x}^{2}}{125}}+{\frac{172\,{x}^{3}}{75}}-{\frac{6\,{x}^{4}}{5}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{3125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34476, size = 36, normalized size = 0.97 \[ -\frac{6}{5} \, x^{4} + \frac{172}{75} \, x^{3} - \frac{183}{125} \, x^{2} - \frac{27}{625} \, x + \frac{1331}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)^3/(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.215387, size = 36, normalized size = 0.97 \[ -\frac{6}{5} \, x^{4} + \frac{172}{75} \, x^{3} - \frac{183}{125} \, x^{2} - \frac{27}{625} \, x + \frac{1331}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)^3/(5*x + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.165411, size = 34, normalized size = 0.92 \[ - \frac{6 x^{4}}{5} + \frac{172 x^{3}}{75} - \frac{183 x^{2}}{125} - \frac{27 x}{625} + \frac{1331 \log{\left (5 x + 3 \right )}}{3125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.207691, size = 38, normalized size = 1.03 \[ -\frac{6}{5} \, x^{4} + \frac{172}{75} \, x^{3} - \frac{183}{125} \, x^{2} - \frac{27}{625} \, x + \frac{1331}{3125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)*(2*x - 1)^3/(5*x + 3),x, algorithm="giac")
[Out]