Optimal. Leaf size=22 \[ 4-\frac {12 e^{-3 x} (2+\log (x))}{x^2}-\log \left (x^2\right ) \]
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Rubi [A] time = 0.68, antiderivative size = 23, normalized size of antiderivative = 1.05, number of steps used = 5, number of rules used = 4, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6741, 12, 6742, 2288} \begin {gather*} -\frac {12 e^{-3 x} (2 x+x \log (x))}{x^3}-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 6741
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^{-3 x} \left (18+36 x-e^{3 x} x^2+12 \log (x)+18 x \log (x)\right )}{x^3} \, dx\\ &=2 \int \frac {e^{-3 x} \left (18+36 x-e^{3 x} x^2+12 \log (x)+18 x \log (x)\right )}{x^3} \, dx\\ &=2 \int \left (-\frac {1}{x}+\frac {6 e^{-3 x} (3+6 x+2 \log (x)+3 x \log (x))}{x^3}\right ) \, dx\\ &=-2 \log (x)+12 \int \frac {e^{-3 x} (3+6 x+2 \log (x)+3 x \log (x))}{x^3} \, dx\\ &=-2 \log (x)-\frac {12 e^{-3 x} (2 x+x \log (x))}{x^3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.30, size = 19, normalized size = 0.86 \begin {gather*} -2 \log (x)-\frac {12 e^{-3 x} (2+\log (x))}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.80, size = 24, normalized size = 1.09 \begin {gather*} -\frac {2 \, {\left ({\left (x^{2} e^{\left (3 \, x\right )} + 6\right )} \log \relax (x) + 12\right )} e^{\left (-3 \, x\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 26, normalized size = 1.18 \begin {gather*} -\frac {2 \, {\left (x^{2} \log \relax (x) + 6 \, e^{\left (-3 \, x\right )} \log \relax (x) + 12 \, e^{\left (-3 \, x\right )}\right )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 34, normalized size = 1.55
method | result | size |
risch | \(-\frac {12 \,{\mathrm e}^{-3 x} \ln \relax (x )}{x^{2}}-\frac {2 \left (\ln \relax (x ) x^{2} {\mathrm e}^{3 x}+12\right ) {\mathrm e}^{-3 x}}{x^{2}}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {12 \, e^{\left (-3 \, x\right )} \log \relax (x)}{x^{2}} - 216 \, \Gamma \left (-1, 3 \, x\right ) - 324 \, \Gamma \left (-2, 3 \, x\right ) + 12 \, \int \frac {e^{\left (-3 \, x\right )}}{x^{3}}\,{d x} - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.30, size = 20, normalized size = 0.91 \begin {gather*} -2\,\ln \relax (x)-\frac {2\,{\mathrm {e}}^{-3\,x}\,\left (6\,\ln \relax (x)+12\right )}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.43, size = 20, normalized size = 0.91 \begin {gather*} - 2 \log {\relax (x )} + \frac {\left (- 12 \log {\relax (x )} - 24\right ) e^{- 3 x}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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