Optimal. Leaf size=24 \[ -\frac {\left (-2+e^4\right ) \left (-1+e^4-x\right ) x^2}{e^6}+\log (x) \]
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Rubi [A]
time = 0.02, antiderivative size = 36, normalized size of antiderivative = 1.50, number of steps
used = 4, number of rules used = 3, integrand size = 44, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.068, Rules used = {6, 12, 14}
\begin {gather*} -\frac {\left (2-e^4\right ) x^3}{e^6}-\frac {\left (2-3 e^4+e^8\right ) x^2}{e^6}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^6+\left (-4-2 e^8\right ) x^2-6 x^3+e^4 \left (6 x^2+3 x^3\right )}{e^6 x} \, dx\\ &=\frac {\int \frac {e^6+\left (-4-2 e^8\right ) x^2-6 x^3+e^4 \left (6 x^2+3 x^3\right )}{x} \, dx}{e^6}\\ &=\frac {\int \left (\frac {e^6}{x}-2 \left (2-3 e^4+e^8\right ) x-3 \left (2-e^4\right ) x^2\right ) \, dx}{e^6}\\ &=-\frac {\left (2-3 e^4+e^8\right ) x^2}{e^6}-\frac {\left (2-e^4\right ) x^3}{e^6}+\log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 42, normalized size = 1.75 \begin {gather*} -\frac {2 x^2}{e^6}+\frac {3 x^2}{e^2}-e^2 x^2-\frac {2 x^3}{e^6}+\frac {x^3}{e^2}+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.34, size = 42, normalized size = 1.75
method | result | size |
norman | \(\left (\left ({\mathrm e}^{4}-2\right ) {\mathrm e}^{-3} x^{3}-\left ({\mathrm e}^{8}-3 \,{\mathrm e}^{4}+2\right ) {\mathrm e}^{-3} x^{2}\right ) {\mathrm e}^{-3}+\ln \left (x \right )\) | \(41\) |
default | \({\mathrm e}^{-6} \left (x^{3} {\mathrm e}^{4}+3 x^{2} {\mathrm e}^{4}-x^{2} {\mathrm e}^{8}-2 x^{3}-2 x^{2}+{\mathrm e}^{6} \ln \left (x \right )\right )\) | \(42\) |
risch | \(-{\mathrm e}^{8} {\mathrm e}^{-6} x^{2}+{\mathrm e}^{4} {\mathrm e}^{-6} x^{3}+3 \,{\mathrm e}^{4} {\mathrm e}^{-6} x^{2}-2 \,{\mathrm e}^{-6} x^{3}-2 \,{\mathrm e}^{-6} x^{2}+\ln \left (x \right )\) | \(46\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 30, normalized size = 1.25 \begin {gather*} {\left (x^{3} {\left (e^{4} - 2\right )} - x^{2} {\left (e^{8} - 3 \, e^{4} + 2\right )} + e^{6} \log \left (x\right )\right )} e^{\left (-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 40, normalized size = 1.67 \begin {gather*} -{\left (2 \, x^{3} + x^{2} e^{8} + 2 \, x^{2} - {\left (x^{3} + 3 \, x^{2}\right )} e^{4} - e^{6} \log \left (x\right )\right )} e^{\left (-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 31, normalized size = 1.29 \begin {gather*} \frac {- x^{3} \cdot \left (2 - e^{4}\right ) - x^{2} \left (- 3 e^{4} + 2 + e^{8}\right ) + e^{6} \log {\left (x \right )}}{e^{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 40, normalized size = 1.67 \begin {gather*} {\left (x^{3} e^{4} - 2 \, x^{3} - x^{2} e^{8} + 3 \, x^{2} e^{4} - 2 \, x^{2} + e^{6} \log \left ({\left | x \right |}\right )\right )} e^{\left (-6\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.09, size = 33, normalized size = 1.38 \begin {gather*} \ln \left (x\right )-\frac {x^2\,{\mathrm {e}}^{-6}\,\left (2\,{\mathrm {e}}^8-6\,{\mathrm {e}}^4+4\right )}{2}+\frac {x^3\,{\mathrm {e}}^{-6}\,\left (3\,{\mathrm {e}}^4-6\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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