Optimal. Leaf size=94 \[ -\frac{3 (47 x+37)}{10 (2 x+3) \left (3 x^2+5 x+2\right )^2}+\frac{10848 x+9293}{50 (2 x+3) \left (3 x^2+5 x+2\right )}+\frac{12946}{125 (2 x+3)}-175 \log (x+1)+\frac{4912}{625} \log (2 x+3)+\frac{104463}{625} \log (3 x+2) \]
[Out]
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Rubi [A] time = 0.158379, antiderivative size = 94, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ -\frac{3 (47 x+37)}{10 (2 x+3) \left (3 x^2+5 x+2\right )^2}+\frac{10848 x+9293}{50 (2 x+3) \left (3 x^2+5 x+2\right )}+\frac{12946}{125 (2 x+3)}-175 \log (x+1)+\frac{4912}{625} \log (2 x+3)+\frac{104463}{625} \log (3 x+2) \]
Antiderivative was successfully verified.
[In] Int[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^3),x]
[Out]
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Rubi in Sympy [A] time = 29.0649, size = 78, normalized size = 0.83 \[ - 175 \log{\left (x + 1 \right )} + \frac{4912 \log{\left (2 x + 3 \right )}}{625} + \frac{104463 \log{\left (3 x + 2 \right )}}{625} - \frac{141 x + 111}{10 \left (2 x + 3\right ) \left (3 x^{2} + 5 x + 2\right )^{2}} + \frac{10848 x + 9293}{50 \left (2 x + 3\right ) \left (3 x^{2} + 5 x + 2\right )} + \frac{12946}{125 \left (2 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2)**3,x)
[Out]
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Mathematica [A] time = 0.0822513, size = 78, normalized size = 0.83 \[ \frac{1}{625} \left (-\frac{75 (201 x+151)}{2 \left (3 x^2+5 x+2\right )^2}+\frac{5 (39462 x+33697)}{6 x^2+10 x+4}-\frac{1040}{2 x+3}+104463 \log (-6 x-4)-109375 \log (-2 (x+1))+4912 \log (2 x+3)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^3),x]
[Out]
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Maple [A] time = 0.02, size = 65, normalized size = 0.7 \[ -{\frac{459}{50\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{8856}{250+375\,x}}+{\frac{104463\,\ln \left ( 2+3\,x \right ) }{625}}-{\frac{208}{375+250\,x}}+{\frac{4912\,\ln \left ( 3+2\,x \right ) }{625}}+3\, \left ( 1+x \right ) ^{-2}+29\, \left ( 1+x \right ) ^{-1}-175\,\ln \left ( 1+x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((5-x)/(3+2*x)^2/(3*x^2+5*x+2)^3,x)
[Out]
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Maxima [A] time = 0.696086, size = 97, normalized size = 1.03 \[ \frac{233028 \, x^{4} + 939480 \, x^{3} + 1368599 \, x^{2} + 855120 \, x + 193723}{250 \,{\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )}} + \frac{104463}{625} \, \log \left (3 \, x + 2\right ) + \frac{4912}{625} \, \log \left (2 \, x + 3\right ) - 175 \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)^3*(2*x + 3)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.271587, size = 197, normalized size = 2.1 \[ \frac{1165140 \, x^{4} + 4697400 \, x^{3} + 6842995 \, x^{2} + 208926 \,{\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 9824 \,{\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )} \log \left (2 \, x + 3\right ) - 218750 \,{\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )} \log \left (x + 1\right ) + 4275600 \, x + 968615}{1250 \,{\left (18 \, x^{5} + 87 \, x^{4} + 164 \, x^{3} + 151 \, x^{2} + 68 \, x + 12\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)^3*(2*x + 3)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.67976, size = 71, normalized size = 0.76 \[ \frac{233028 x^{4} + 939480 x^{3} + 1368599 x^{2} + 855120 x + 193723}{4500 x^{5} + 21750 x^{4} + 41000 x^{3} + 37750 x^{2} + 17000 x + 3000} + \frac{104463 \log{\left (x + \frac{2}{3} \right )}}{625} - 175 \log{\left (x + 1 \right )} + \frac{4912 \log{\left (x + \frac{3}{2} \right )}}{625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5-x)/(3+2*x)**2/(3*x**2+5*x+2)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.268725, size = 128, normalized size = 1.36 \[ -\frac{208}{125 \,{\left (2 \, x + 3\right )}} - \frac{2 \,{\left (\frac{168231}{2 \, x + 3} - \frac{211036}{{\left (2 \, x + 3\right )}^{2}} + \frac{82447}{{\left (2 \, x + 3\right )}^{3}} - 42642\right )}}{125 \,{\left (\frac{5}{2 \, x + 3} - 3\right )}^{2}{\left (\frac{1}{2 \, x + 3} - 1\right )}^{2}} - 175 \,{\rm ln}\left ({\left | -\frac{1}{2 \, x + 3} + 1 \right |}\right ) + \frac{104463}{625} \,{\rm ln}\left ({\left | -\frac{5}{2 \, x + 3} + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(x - 5)/((3*x^2 + 5*x + 2)^3*(2*x + 3)^2),x, algorithm="giac")
[Out]