Optimal. Leaf size=48 \[ -\frac{50 x^4}{9}+\frac{980 x^3}{81}-\frac{313 x^2}{27}+\frac{2323 x}{243}-\frac{343}{729 (3 x+2)}-\frac{3724}{729} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0625068, antiderivative size = 48, 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 \[ -\frac{50 x^4}{9}+\frac{980 x^3}{81}-\frac{313 x^2}{27}+\frac{2323 x}{243}-\frac{343}{729 (3 x+2)}-\frac{3724}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{50 x^{4}}{9} + \frac{980 x^{3}}{81} - \frac{3724 \log{\left (3 x + 2 \right )}}{729} + \int \frac{2323}{243}\, dx - \frac{626 \int x\, dx}{27} - \frac{343}{729 \left (3 x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**2,x)
[Out]
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Mathematica [A] time = 0.0487891, size = 49, normalized size = 1.02 \[ \frac{-36450 x^5+55080 x^4-23139 x^3+12015 x^2+148152 x-11172 (3 x+2) \log (30 x+20)+69863}{2187 (3 x+2)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)^3*(3 + 5*x)^2)/(2 + 3*x)^2,x]
[Out]
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Maple [A] time = 0.009, size = 37, normalized size = 0.8 \[{\frac{2323\,x}{243}}-{\frac{313\,{x}^{2}}{27}}+{\frac{980\,{x}^{3}}{81}}-{\frac{50\,{x}^{4}}{9}}-{\frac{343}{1458+2187\,x}}-{\frac{3724\,\ln \left ( 2+3\,x \right ) }{729}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)^3*(3+5*x)^2/(2+3*x)^2,x)
[Out]
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Maxima [A] time = 1.33544, size = 49, normalized size = 1.02 \[ -\frac{50}{9} \, x^{4} + \frac{980}{81} \, x^{3} - \frac{313}{27} \, x^{2} + \frac{2323}{243} \, x - \frac{343}{729 \,{\left (3 \, x + 2\right )}} - \frac{3724}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.209077, size = 63, normalized size = 1.31 \[ -\frac{12150 \, x^{5} - 18360 \, x^{4} + 7713 \, x^{3} - 4005 \, x^{2} + 3724 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 13938 \, x + 343}{729 \,{\left (3 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.246106, size = 41, normalized size = 0.85 \[ - \frac{50 x^{4}}{9} + \frac{980 x^{3}}{81} - \frac{313 x^{2}}{27} + \frac{2323 x}{243} - \frac{3724 \log{\left (3 x + 2 \right )}}{729} - \frac{343}{2187 x + 1458} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)**3*(3+5*x)**2/(2+3*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.212702, size = 89, normalized size = 1.85 \[ \frac{1}{2187} \,{\left (3 \, x + 2\right )}^{4}{\left (\frac{2180}{3 \, x + 2} - \frac{12297}{{\left (3 \, x + 2\right )}^{2}} + \frac{34797}{{\left (3 \, x + 2\right )}^{3}} - 150\right )} - \frac{343}{729 \,{\left (3 \, x + 2\right )}} + \frac{3724}{729} \,{\rm ln}\left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(5*x + 3)^2*(2*x - 1)^3/(3*x + 2)^2,x, algorithm="giac")
[Out]