Optimal. Leaf size=36 \[ \frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+405 \log (x+3) \]
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Rubi [A] time = 0.0151688, antiderivative size = 36, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {43} \[ \frac{x^4}{4}-2 x^3+\frac{27 x^2}{2}-108 x+\frac{243}{x+3}+405 \log (x+3) \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin{align*} \int \frac{x^5}{(3+x)^2} \, dx &=\int \left (-108+27 x-6 x^2+x^3-\frac{243}{(3+x)^2}+\frac{405}{3+x}\right ) \, dx\\ &=-108 x+\frac{27 x^2}{2}-2 x^3+\frac{x^4}{4}+\frac{243}{3+x}+405 \log (3+x)\\ \end{align*}
Mathematica [A] time = 0.0136431, size = 36, normalized size = 1. \[ \frac{1}{4} \left (x^4-8 x^3+54 x^2-432 x+\frac{972}{x+3}-2079\right )+405 \log (x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 33, normalized size = 0.9 \begin{align*} -108\,x+{\frac{27\,{x}^{2}}{2}}-2\,{x}^{3}+{\frac{{x}^{4}}{4}}+243\, \left ( 3+x \right ) ^{-1}+405\,\ln \left ( 3+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.929725, size = 43, normalized size = 1.19 \begin{align*} \frac{1}{4} \, x^{4} - 2 \, x^{3} + \frac{27}{2} \, x^{2} - 108 \, x + \frac{243}{x + 3} + 405 \, \log \left (x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.58525, size = 117, normalized size = 3.25 \begin{align*} \frac{x^{5} - 5 \, x^{4} + 30 \, x^{3} - 270 \, x^{2} + 1620 \,{\left (x + 3\right )} \log \left (x + 3\right ) - 1296 \, x + 972}{4 \,{\left (x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.080228, size = 31, normalized size = 0.86 \begin{align*} \frac{x^{4}}{4} - 2 x^{3} + \frac{27 x^{2}}{2} - 108 x + 405 \log{\left (x + 3 \right )} + \frac{243}{x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05162, size = 61, normalized size = 1.69 \begin{align*} -\frac{1}{4} \,{\left (x + 3\right )}^{4}{\left (\frac{20}{x + 3} - \frac{180}{{\left (x + 3\right )}^{2}} + \frac{1080}{{\left (x + 3\right )}^{3}} - 1\right )} + \frac{243}{x + 3} + 405 \, \log \left ({\left | x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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