Optimal. Leaf size=17 \[ -\frac {2}{e^{14} x}-x+e^5 x \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 2, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {12, 14} \begin {gather*} -\left (\left (1-e^5\right ) x\right )-\frac {2}{e^{14} 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 {2 e^2+e^{16} \left (-x^2+e^5 x^2\right )}{x^2} \, dx}{e^{16}}\\ &=\frac {\int \left (e^{16} \left (-1+e^5\right )+\frac {2 e^2}{x^2}\right ) \, dx}{e^{16}}\\ &=-\frac {2}{e^{14} x}-\left (1-e^5\right ) x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -\frac {2}{e^{14} x}-x+e^5 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.59, size = 21, normalized size = 1.24 \begin {gather*} \frac {{\left (x^{2} e^{19} - x^{2} e^{14} - 2\right )} e^{\left (-14\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.26, size = 20, normalized size = 1.18 \begin {gather*} {\left (x e^{21} - x e^{16} - \frac {2 \, e^{2}}{x}\right )} e^{\left (-16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 22, normalized size = 1.29
method | result | size |
norman | \(\frac {\left ({\mathrm e}^{5}-1\right ) x^{2}-2 \,{\mathrm e}^{-16} {\mathrm e}^{2}}{x}\) | \(22\) |
risch | \({\mathrm e}^{-16} x \,{\mathrm e}^{21}-{\mathrm e}^{-16} x \,{\mathrm e}^{16}-\frac {2 \,{\mathrm e}^{-14}}{x}\) | \(22\) |
default | \({\mathrm e}^{-16} \left (x \,{\mathrm e}^{21}-x \,{\mathrm e}^{16}-\frac {2 \,{\mathrm e}^{2}}{x}\right )\) | \(23\) |
gosper | \(\frac {\left ({\mathrm e}^{5} {\mathrm e}^{16} x^{2}-x^{2} {\mathrm e}^{16}-2 \,{\mathrm e}^{2}\right ) {\mathrm e}^{-16}}{x}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 20, normalized size = 1.18 \begin {gather*} {\left (x {\left (e^{21} - e^{16}\right )} - \frac {2 \, e^{2}}{x}\right )} e^{\left (-16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 14, normalized size = 0.82 \begin {gather*} x\,\left ({\mathrm {e}}^5-1\right )-\frac {2\,{\mathrm {e}}^{-14}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 15, normalized size = 0.88 \begin {gather*} \frac {- x \left (- e^{19} + e^{14}\right ) - \frac {2}{x}}{e^{14}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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