Optimal. Leaf size=22 \[ 5 e+(3-x) \left (-6-\frac {9}{x}-x\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {14} \begin {gather*} -x^3-9 x^2+\frac {243}{x^2}-18 x+\frac {243}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-18-\frac {486}{x^3}-\frac {243}{x^2}-18 x-3 x^2\right ) \, dx\\ &=\frac {243}{x^2}+\frac {243}{x}-18 x-9 x^2-x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.09 \begin {gather*} \frac {243}{x^2}+\frac {243}{x}-18 x-9 x^2-x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 23, normalized size = 1.05 \begin {gather*} -\frac {x^{5} + 9 \, x^{4} + 18 \, x^{3} - 243 \, x - 243}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 22, normalized size = 1.00 \begin {gather*} -x^{3} - 9 \, x^{2} - 18 \, x + \frac {243 \, {\left (x + 1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 24, normalized size = 1.09
method | result | size |
gosper | \(-\frac {x^{5}+9 x^{4}+18 x^{3}-243 x -243}{x^{2}}\) | \(24\) |
risch | \(-x^{3}-9 x^{2}-18 x +\frac {243 x +243}{x^{2}}\) | \(24\) |
default | \(-x^{3}-9 x^{2}-18 x +\frac {243}{x}+\frac {243}{x^{2}}\) | \(25\) |
norman | \(\frac {-x^{5}-9 x^{4}-18 x^{3}+243 x +243}{x^{2}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 22, normalized size = 1.00 \begin {gather*} -x^{3} - 9 \, x^{2} - 18 \, x + \frac {243 \, {\left (x + 1\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 23, normalized size = 1.05 \begin {gather*} \frac {243\,x+243}{x^2}-18\,x-9\,x^2-x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 22, normalized size = 1.00 \begin {gather*} - x^{3} - 9 x^{2} - 18 x - \frac {- 243 x - 243}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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