Optimal. Leaf size=43 \[ -\frac{2611 x+2449}{27 \left (3 x^2+5 x+2\right )}-\frac{8 x}{9}+71 \log (x+1)-\frac{1825}{27} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.094482, antiderivative size = 43, normalized size of antiderivative = 1., number of steps used = 7, number of rules used = 5, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ -\frac{2611 x+2449}{27 \left (3 x^2+5 x+2\right )}-\frac{8 x}{9}+71 \log (x+1)-\frac{1825}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{\left (2 x + 3\right )^{2} \left (139 x + 121\right )}{3 \left (3 x^{2} + 5 x + 2\right )} + 71 \log{\left (x + 1 \right )} - \frac{1825 \log{\left (3 x + 2 \right )}}{27} + \frac{\int \frac{548}{3}\, dx}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2)**2,x)
[Out]
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Mathematica [A] time = 0.0611932, size = 47, normalized size = 1.09 \[ -\frac{2611 x+2449}{81 x^2+135 x+54}-\frac{4}{9} (2 x+3)-\frac{1825}{27} \log (-6 x-4)+71 \log (-2 (x+1)) \]
Antiderivative was successfully verified.
[In] Integrate[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^2,x]
[Out]
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Maple [A] time = 0.013, size = 35, normalized size = 0.8 \[ -{\frac{8\,x}{9}}-{\frac{2125}{54+81\,x}}-{\frac{1825\,\ln \left ( 2+3\,x \right ) }{27}}-6\, \left ( 1+x \right ) ^{-1}+71\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)*(3+2*x)^3/(3*x^2+5*x+2)^2,x)
[Out]
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Maxima [A] time = 0.692168, size = 50, normalized size = 1.16 \[ -\frac{8}{9} \, x - \frac{2611 \, x + 2449}{27 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}} - \frac{1825}{27} \, \log \left (3 \, x + 2\right ) + 71 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^3*(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.265181, size = 85, normalized size = 1.98 \[ -\frac{72 \, x^{3} + 120 \, x^{2} + 1825 \,{\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 1917 \,{\left (3 \, x^{2} + 5 \, x + 2\right )} \log \left (x + 1\right ) + 2659 \, x + 2449}{27 \,{\left (3 \, x^{2} + 5 \, x + 2\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^3*(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.395492, size = 36, normalized size = 0.84 \[ - \frac{8 x}{9} - \frac{2611 x + 2449}{81 x^{2} + 135 x + 54} - \frac{1825 \log{\left (x + \frac{2}{3} \right )}}{27} + 71 \log{\left (x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)*(3+2*x)**3/(3*x**2+5*x+2)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.381487, size = 53, normalized size = 1.23 \[ -\frac{8}{9} \, x - \frac{2611 \, x + 2449}{27 \,{\left (3 \, x + 2\right )}{\left (x + 1\right )}} - \frac{1825}{27} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + 71 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(2*x + 3)^3*(x - 5)/(3*x^2 + 5*x + 2)^2,x, algorithm="giac")
[Out]