Optimal. Leaf size=51 \[ -\frac{36 x^6}{5}+\frac{108 x^5}{125}+\frac{2313 x^4}{250}-\frac{5003 x^3}{1875}-\frac{26241 x^2}{6250}+\frac{41223 x}{15625}+\frac{1331 \log (5 x+3)}{78125} \]
[Out]
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Rubi [A] time = 0.0568837, antiderivative size = 51, 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 \[ -\frac{36 x^6}{5}+\frac{108 x^5}{125}+\frac{2313 x^4}{250}-\frac{5003 x^3}{1875}-\frac{26241 x^2}{6250}+\frac{41223 x}{15625}+\frac{1331 \log (5 x+3)}{78125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{36 x^{6}}{5} + \frac{108 x^{5}}{125} + \frac{2313 x^{4}}{250} - \frac{5003 x^{3}}{1875} + \frac{1331 \log{\left (5 x + 3 \right )}}{78125} + \int \frac{41223}{15625}\, dx - \frac{26241 \int x\, dx}{3125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**3/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0191532, size = 42, normalized size = 0.82 \[ \frac{-16875000 x^6+2025000 x^5+21684375 x^4-6253750 x^3-9840375 x^2+6183450 x+39930 \log (5 x+3)+4036284}{2343750} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x)^3)/(3 + 5*x),x]
[Out]
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Maple [A] time = 0.004, size = 38, normalized size = 0.8 \[{\frac{41223\,x}{15625}}-{\frac{26241\,{x}^{2}}{6250}}-{\frac{5003\,{x}^{3}}{1875}}+{\frac{2313\,{x}^{4}}{250}}+{\frac{108\,{x}^{5}}{125}}-{\frac{36\,{x}^{6}}{5}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{78125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^3/(3+5*x),x)
[Out]
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Maxima [A] time = 1.3497, size = 50, normalized size = 0.98 \[ -\frac{36}{5} \, x^{6} + \frac{108}{125} \, x^{5} + \frac{2313}{250} \, x^{4} - \frac{5003}{1875} \, x^{3} - \frac{26241}{6250} \, x^{2} + \frac{41223}{15625} \, x + \frac{1331}{78125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)^3/(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219454, size = 50, normalized size = 0.98 \[ -\frac{36}{5} \, x^{6} + \frac{108}{125} \, x^{5} + \frac{2313}{250} \, x^{4} - \frac{5003}{1875} \, x^{3} - \frac{26241}{6250} \, x^{2} + \frac{41223}{15625} \, x + \frac{1331}{78125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)^3/(5*x + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.187383, size = 48, normalized size = 0.94 \[ - \frac{36 x^{6}}{5} + \frac{108 x^{5}}{125} + \frac{2313 x^{4}}{250} - \frac{5003 x^{3}}{1875} - \frac{26241 x^{2}}{6250} + \frac{41223 x}{15625} + \frac{1331 \log{\left (5 x + 3 \right )}}{78125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**3/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.206822, size = 51, normalized size = 1. \[ -\frac{36}{5} \, x^{6} + \frac{108}{125} \, x^{5} + \frac{2313}{250} \, x^{4} - \frac{5003}{1875} \, x^{3} - \frac{26241}{6250} \, x^{2} + \frac{41223}{15625} \, x + \frac{1331}{78125} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^3*(2*x - 1)^3/(5*x + 3),x, algorithm="giac")
[Out]