Optimal. Leaf size=44 \[ -\frac{72 x^5}{25}+\frac{69 x^4}{25}+\frac{622 x^3}{375}-\frac{3741 x^2}{1250}+\frac{3723 x}{3125}+\frac{1331 \log (5 x+3)}{15625} \]
[Out]
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Rubi [A] time = 0.0470215, antiderivative size = 44, 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 \[ -\frac{72 x^5}{25}+\frac{69 x^4}{25}+\frac{622 x^3}{375}-\frac{3741 x^2}{1250}+\frac{3723 x}{3125}+\frac{1331 \log (5 x+3)}{15625} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{72 x^{5}}{25} + \frac{69 x^{4}}{25} + \frac{622 x^{3}}{375} + \frac{1331 \log{\left (5 x + 3 \right )}}{15625} + \int \frac{3723}{3125}\, dx - \frac{3741 \int x\, dx}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(2+3*x)**2/(3+5*x),x)
[Out]
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Mathematica [A] time = 0.0188953, size = 37, normalized size = 0.84 \[ \frac{-1350000 x^5+1293750 x^4+777500 x^3-1402875 x^2+558450 x+39930 \log (5 x+3)+735399}{468750} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(2 + 3*x)^2)/(3 + 5*x),x]
[Out]
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Maple [A] time = 0.003, size = 33, normalized size = 0.8 \[{\frac{3723\,x}{3125}}-{\frac{3741\,{x}^{2}}{1250}}+{\frac{622\,{x}^{3}}{375}}+{\frac{69\,{x}^{4}}{25}}-{\frac{72\,{x}^{5}}{25}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{15625}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(2+3*x)^2/(3+5*x),x)
[Out]
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Maxima [A] time = 1.34339, size = 43, normalized size = 0.98 \[ -\frac{72}{25} \, x^{5} + \frac{69}{25} \, x^{4} + \frac{622}{375} \, x^{3} - \frac{3741}{1250} \, x^{2} + \frac{3723}{3125} \, x + \frac{1331}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)^3/(5*x + 3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.205085, size = 43, normalized size = 0.98 \[ -\frac{72}{25} \, x^{5} + \frac{69}{25} \, x^{4} + \frac{622}{375} \, x^{3} - \frac{3741}{1250} \, x^{2} + \frac{3723}{3125} \, x + \frac{1331}{15625} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)^3/(5*x + 3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.199147, size = 41, normalized size = 0.93 \[ - \frac{72 x^{5}}{25} + \frac{69 x^{4}}{25} + \frac{622 x^{3}}{375} - \frac{3741 x^{2}}{1250} + \frac{3723 x}{3125} + \frac{1331 \log{\left (5 x + 3 \right )}}{15625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(2+3*x)**2/(3+5*x),x)
[Out]
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GIAC/XCAS [A] time = 0.212685, size = 45, normalized size = 1.02 \[ -\frac{72}{25} \, x^{5} + \frac{69}{25} \, x^{4} + \frac{622}{375} \, x^{3} - \frac{3741}{1250} \, x^{2} + \frac{3723}{3125} \, x + \frac{1331}{15625} \,{\rm ln}\left ({\left | 5 \, x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^2*(2*x - 1)^3/(5*x + 3),x, algorithm="giac")
[Out]