Optimal. Leaf size=20 \[ -x+\frac {x \left (-\frac {3}{x}+x^4\right )^2}{e} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.35, number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {12, 14} \begin {gather*} \frac {x^9}{e}-\frac {6 x^4}{e}-x+\frac {9}{e x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {-9-e x^2-24 x^5+9 x^{10}}{x^2} \, dx}{e}\\ &=\frac {\int \left (-e-\frac {9}{x^2}-24 x^3+9 x^8\right ) \, dx}{e}\\ &=\frac {9}{e x}-x-\frac {6 x^4}{e}+\frac {x^9}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 24, normalized size = 1.20 \begin {gather*} -\frac {-\frac {9}{x}+e x+6 x^4-x^9}{e} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 23, normalized size = 1.15 \begin {gather*} \frac {{\left (x^{10} - 6 \, x^{5} - x^{2} e + 9\right )} e^{\left (-1\right )}}{x} \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 = 1.10 \begin {gather*} {\left (x^{9} - 6 \, x^{4} - x e + \frac {9}{x}\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 25, normalized size = 1.25
method | result | size |
default | \({\mathrm e}^{-1} \left (x^{9}-6 x^{4}-x \,{\mathrm e}+\frac {9}{x}\right )\) | \(25\) |
risch | \({\mathrm e}^{-1} x^{9}-6 x^{4} {\mathrm e}^{-1}-x +\frac {9 \,{\mathrm e}^{-1}}{x}\) | \(25\) |
gosper | \(-\frac {\left (-x^{10}-9+6 x^{5}+x^{2} {\mathrm e}\right ) {\mathrm e}^{-1}}{x}\) | \(28\) |
norman | \(\frac {{\mathrm e}^{-1} x^{10}-x^{2}+9 \,{\mathrm e}^{-1}-6 \,{\mathrm e}^{-1} x^{5}}{x}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 22, normalized size = 1.10 \begin {gather*} {\left (x^{9} - 6 \, x^{4} - x e + \frac {9}{x}\right )} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.79, size = 24, normalized size = 1.20 \begin {gather*} \frac {9\,{\mathrm {e}}^{-1}}{x}-x-6\,x^4\,{\mathrm {e}}^{-1}+x^9\,{\mathrm {e}}^{-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 19, normalized size = 0.95 \begin {gather*} \frac {x^{9} - 6 x^{4} - e x + \frac {9}{x}}{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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