Optimal. Leaf size=15 \[ \frac {196 e \left (1+\frac {1+x}{e^2}\right )}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 2, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 30} \begin {gather*} \frac {196 \left (1+e^2\right )}{e x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {\left (196 \left (1+e^2\right )\right ) \int \frac {1}{x^2} \, dx}{e}\\ &=\frac {196 \left (1+e^2\right )}{e x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 0.87 \begin {gather*} \frac {196 \left (1+e^2\right )}{e x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 11, normalized size = 0.73 \begin {gather*} \frac {196 \, {\left (e^{2} + 1\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 = 0.13, size = 12, normalized size = 0.80 \begin {gather*} \frac {196 \, {\left (e^{3} + e\right )} e^{\left (-2\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 16, normalized size = 1.07
method | result | size |
gosper | \(\frac {196 \,{\mathrm e} \left ({\mathrm e}^{2}+1\right ) {\mathrm e}^{-2}}{x}\) | \(16\) |
norman | \(\frac {196 \,{\mathrm e} \left ({\mathrm e}^{2}+1\right ) {\mathrm e}^{-2}}{x}\) | \(16\) |
risch | \(\frac {196 \,{\mathrm e}^{-2} {\mathrm e}^{3}}{x}+\frac {196 \,{\mathrm e}^{-2} {\mathrm e}}{x}\) | \(20\) |
default | \(-\frac {196 \left (-{\mathrm e} \,{\mathrm e}^{2}-{\mathrm e}\right ) {\mathrm e}^{-2}}{x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 12, normalized size = 0.80 \begin {gather*} \frac {196 \, {\left (e^{3} + e\right )} e^{\left (-2\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 11, normalized size = 0.73 \begin {gather*} \frac {196\,{\mathrm {e}}^{-1}\,\left ({\mathrm {e}}^2+1\right )}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 14, normalized size = 0.93 \begin {gather*} - \frac {- 196 e^{2} - 196}{e x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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