Optimal. Leaf size=46 \[ \frac{1}{x+2}+\frac{5}{4 (x+3)}+\frac{1}{4 (x+3)^2}+\frac{1}{8} \log (x+1)+2 \log (x+2)-\frac{17}{8} \log (x+3) \]
[Out]
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Rubi [A] time = 0.0595168, antiderivative size = 46, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ \frac{1}{x+2}+\frac{5}{4 (x+3)}+\frac{1}{4 (x+3)^2}+\frac{1}{8} \log (x+1)+2 \log (x+2)-\frac{17}{8} \log (x+3) \]
Antiderivative was successfully verified.
[In] Int[1/((1 + x)*(2 + x)^2*(3 + x)^3),x]
[Out]
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Rubi in Sympy [A] time = 7.23463, size = 41, normalized size = 0.89 \[ \frac{\log{\left (x + 1 \right )}}{8} + 2 \log{\left (x + 2 \right )} - \frac{17 \log{\left (x + 3 \right )}}{8} + \frac{5}{4 \left (x + 3\right )} + \frac{1}{4 \left (x + 3\right )^{2}} + \frac{1}{x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1+x)/(2+x)**2/(3+x)**3,x)
[Out]
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Mathematica [A] time = 0.0266584, size = 44, normalized size = 0.96 \[ \frac{1}{8} \left (\frac{8}{x+2}+\frac{10}{x+3}+\frac{2}{(x+3)^2}+\log (-x-1)+16 \log (x+2)-17 \log (x+3)\right ) \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 + x)*(2 + x)^2*(3 + x)^3),x]
[Out]
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Maple [A] time = 0.016, size = 39, normalized size = 0.9 \[ \left ( 2+x \right ) ^{-1}+{\frac{1}{4\, \left ( 3+x \right ) ^{2}}}+{\frac{5}{12+4\,x}}+{\frac{\ln \left ( 1+x \right ) }{8}}+2\,\ln \left ( 2+x \right ) -{\frac{17\,\ln \left ( 3+x \right ) }{8}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1+x)/(2+x)^2/(3+x)^3,x)
[Out]
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Maxima [A] time = 0.780402, size = 62, normalized size = 1.35 \[ \frac{9 \, x^{2} + 50 \, x + 68}{4 \,{\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )}} - \frac{17}{8} \, \log \left (x + 3\right ) + 2 \, \log \left (x + 2\right ) + \frac{1}{8} \, \log \left (x + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 3)^3*(x + 2)^2*(x + 1)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.275284, size = 112, normalized size = 2.43 \[ \frac{18 \, x^{2} - 17 \,{\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 3\right ) + 16 \,{\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 2\right ) +{\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 1\right ) + 100 \, x + 136}{8 \,{\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 3)^3*(x + 2)^2*(x + 1)),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.508482, size = 46, normalized size = 1. \[ \frac{9 x^{2} + 50 x + 68}{4 x^{3} + 32 x^{2} + 84 x + 72} + \frac{\log{\left (x + 1 \right )}}{8} + 2 \log{\left (x + 2 \right )} - \frac{17 \log{\left (x + 3 \right )}}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1+x)/(2+x)**2/(3+x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.260756, size = 70, normalized size = 1.52 \[ \frac{1}{x + 2} - \frac{\frac{7}{x + 2} + 6}{4 \,{\left (\frac{1}{x + 2} + 1\right )}^{2}} + \frac{1}{8} \,{\rm ln}\left ({\left | -\frac{1}{x + 2} + 1 \right |}\right ) - \frac{17}{8} \,{\rm ln}\left ({\left | -\frac{1}{x + 2} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((x + 3)^3*(x + 2)^2*(x + 1)),x, algorithm="giac")
[Out]