Optimal. Leaf size=49 \[ -\frac{99}{25 (2 x+3)}-\frac{13}{10 (2 x+3)^2}-6 \log (x+1)+\frac{597}{125} \log (2 x+3)+\frac{153}{125} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.0711207, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ -\frac{99}{25 (2 x+3)}-\frac{13}{10 (2 x+3)^2}-6 \log (x+1)+\frac{597}{125} \log (2 x+3)+\frac{153}{125} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)),x]
[Out]
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Rubi in Sympy [A] time = 14.4125, size = 42, normalized size = 0.86 \[ - 6 \log{\left (x + 1 \right )} + \frac{597 \log{\left (2 x + 3 \right )}}{125} + \frac{153 \log{\left (3 x + 2 \right )}}{125} - \frac{99}{25 \left (2 x + 3\right )} - \frac{13}{10 \left (2 x + 3\right )^{2}} \]
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),x)
[Out]
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Mathematica [A] time = 0.0432876, size = 47, normalized size = 0.96 \[ \frac{1}{250} \left (-\frac{990}{2 x+3}-\frac{325}{(2 x+3)^2}+306 \log (-6 x-4)-1500 \log (-2 (x+1))+1194 \log (2 x+3)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)),x]
[Out]
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Maple [A] time = 0.013, size = 42, normalized size = 0.9 \[ -{\frac{13}{10\, \left ( 3+2\,x \right ) ^{2}}}-{\frac{99}{75+50\,x}}-6\,\ln \left ( 1+x \right ) +{\frac{597\,\ln \left ( 3+2\,x \right ) }{125}}+{\frac{153\,\ln \left ( 2+3\,x \right ) }{125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)/(3+2*x)^3/(3*x^2+5*x+2),x)
[Out]
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Maxima [A] time = 0.685694, size = 57, normalized size = 1.16 \[ -\frac{396 \, x + 659}{50 \,{\left (4 \, x^{2} + 12 \, x + 9\right )}} + \frac{153}{125} \, \log \left (3 \, x + 2\right ) + \frac{597}{125} \, \log \left (2 \, x + 3\right ) - 6 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)*(2*x + 3)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.2719, size = 96, normalized size = 1.96 \[ \frac{306 \,{\left (4 \, x^{2} + 12 \, x + 9\right )} \log \left (3 \, x + 2\right ) + 1194 \,{\left (4 \, x^{2} + 12 \, x + 9\right )} \log \left (2 \, x + 3\right ) - 1500 \,{\left (4 \, x^{2} + 12 \, x + 9\right )} \log \left (x + 1\right ) - 1980 \, x - 3295}{250 \,{\left (4 \, x^{2} + 12 \, x + 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)*(2*x + 3)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.474504, size = 41, normalized size = 0.84 \[ - \frac{396 x + 659}{200 x^{2} + 600 x + 450} + \frac{153 \log{\left (x + \frac{2}{3} \right )}}{125} - 6 \log{\left (x + 1 \right )} + \frac{597 \log{\left (x + \frac{3}{2} \right )}}{125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)/(3+2*x)**3/(3*x**2+5*x+2),x)
[Out]
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GIAC/XCAS [A] time = 0.277163, size = 54, normalized size = 1.1 \[ -\frac{396 \, x + 659}{50 \,{\left (2 \, x + 3\right )}^{2}} + \frac{153}{125} \,{\rm ln}\left ({\left | 3 \, x + 2 \right |}\right ) + \frac{597}{125} \,{\rm ln}\left ({\left | 2 \, x + 3 \right |}\right ) - 6 \,{\rm ln}\left ({\left | x + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)*(2*x + 3)^3),x, algorithm="giac")
[Out]