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 = 0.02, antiderivative size = 36, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 36, normalized size = 1.00 \[ \frac {1}{4} \left (x^4-8 x^3+54 x^2-432 x+\frac {972}{x+3}-2079\right )+405 \log (x+3) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.00, size = 39, normalized size = 1.08 \[ \frac {x^5-5 x^4+30 x^3-270 x^2-1296 x+972}{4 (x+3)}+405 \log (x+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 1.28, size = 39, normalized size = 1.08 \[ \frac {x^{5} - 5 \, x^{4} + 30 \, x^{3} - 270 \, x^{2} + 1620 \, {\left (x + 3\right )} \log \left (x + 3\right ) - 1296 \, x + 972}{4 \, {\left (x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 45, normalized size = 1.25 \[ -\frac {1}{4} \, {\left (x + 3\right )}^{4} {\left (\frac {20}{x + 3} - \frac {180}{{\left (x + 3\right )}^{2}} + \frac {1080}{{\left (x + 3\right )}^{3}} - 1\right )} + \frac {243}{x + 3} + 405 \, \log \left ({\left | x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 33, normalized size = 0.92
method | result | size |
default | \(-108 x +\frac {27 x^{2}}{2}-2 x^{3}+\frac {x^{4}}{4}+\frac {243}{3+x}+405 \ln \left (3+x \right )\) | \(33\) |
risch | \(-108 x +\frac {27 x^{2}}{2}-2 x^{3}+\frac {x^{4}}{4}+\frac {243}{3+x}+405 \ln \left (3+x \right )\) | \(33\) |
norman | \(\frac {-\frac {135}{2} x^{2}+\frac {15}{2} x^{3}-\frac {5}{4} x^{4}+\frac {1}{4} x^{5}+1215}{3+x}+405 \ln \left (3+x \right )\) | \(36\) |
meijerg | \(-\frac {9 x \left (-\frac {1}{27} x^{4}+\frac {5}{27} x^{3}-\frac {10}{9} x^{2}+10 x +60\right )}{4 \left (1+\frac {x}{3}\right )}+405 \ln \left (1+\frac {x}{3}\right )\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 32, normalized size = 0.89 \[ \frac {1}{4} \, x^{4} - 2 \, x^{3} + \frac {27}{2} \, x^{2} - 108 \, x + \frac {243}{x + 3} + 405 \, \log \left (x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.00, size = 32, normalized size = 0.89 \[ 405\,\ln \left (x+3\right )-108\,x+\frac {243}{x+3}+\frac {27\,x^2}{2}-2\,x^3+\frac {x^4}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 31, normalized size = 0.86 \[ \frac {x^{4}}{4} - 2 x^{3} + \frac {27 x^{2}}{2} - 108 x + 405 \log {\left (x + 3 \right )} + \frac {243}{x + 3} \]
Verification of antiderivative is not currently implemented for this CAS.
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