Optimal. Leaf size=17 \[ \frac {-195+x+\log (x)}{\frac {e^x}{3}+x} \]
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Rubi [F] time = 1.46, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1764 x+e^x \left (3+588 x-3 x^2\right )+\left (-9 x-3 e^x x\right ) \log (x)}{e^{2 x} x+6 e^x x^2+9 x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (588 x-e^x \left (-1-196 x+x^2\right )-\left (3+e^x\right ) x \log (x)\right )}{x \left (e^x+3 x\right )^2} \, dx\\ &=3 \int \frac {588 x-e^x \left (-1-196 x+x^2\right )-\left (3+e^x\right ) x \log (x)}{x \left (e^x+3 x\right )^2} \, dx\\ &=3 \int \left (\frac {3 (-1+x) (-195+x+\log (x))}{\left (e^x+3 x\right )^2}-\frac {-1-196 x+x^2+x \log (x)}{x \left (e^x+3 x\right )}\right ) \, dx\\ &=-\left (3 \int \frac {-1-196 x+x^2+x \log (x)}{x \left (e^x+3 x\right )} \, dx\right )+9 \int \frac {(-1+x) (-195+x+\log (x))}{\left (e^x+3 x\right )^2} \, dx\\ &=-\left (3 \int \left (-\frac {196}{e^x+3 x}-\frac {1}{x \left (e^x+3 x\right )}+\frac {x}{e^x+3 x}+\frac {\log (x)}{e^x+3 x}\right ) \, dx\right )+9 \int \left (-\frac {-195+x+\log (x)}{\left (e^x+3 x\right )^2}+\frac {x (-195+x+\log (x))}{\left (e^x+3 x\right )^2}\right ) \, dx\\ &=3 \int \frac {1}{x \left (e^x+3 x\right )} \, dx-3 \int \frac {x}{e^x+3 x} \, dx-3 \int \frac {\log (x)}{e^x+3 x} \, dx-9 \int \frac {-195+x+\log (x)}{\left (e^x+3 x\right )^2} \, dx+9 \int \frac {x (-195+x+\log (x))}{\left (e^x+3 x\right )^2} \, dx+588 \int \frac {1}{e^x+3 x} \, dx\\ &=3 \int \frac {1}{x \left (e^x+3 x\right )} \, dx-3 \int \frac {x}{e^x+3 x} \, dx+3 \int \frac {\int \frac {1}{e^x+3 x} \, dx}{x} \, dx-9 \int \left (-\frac {195}{\left (e^x+3 x\right )^2}+\frac {x}{\left (e^x+3 x\right )^2}+\frac {\log (x)}{\left (e^x+3 x\right )^2}\right ) \, dx+9 \int \left (-\frac {195 x}{\left (e^x+3 x\right )^2}+\frac {x^2}{\left (e^x+3 x\right )^2}+\frac {x \log (x)}{\left (e^x+3 x\right )^2}\right ) \, dx+588 \int \frac {1}{e^x+3 x} \, dx-(3 \log (x)) \int \frac {1}{e^x+3 x} \, dx\\ &=3 \int \frac {1}{x \left (e^x+3 x\right )} \, dx-3 \int \frac {x}{e^x+3 x} \, dx+3 \int \frac {\int \frac {1}{e^x+3 x} \, dx}{x} \, dx-9 \int \frac {x}{\left (e^x+3 x\right )^2} \, dx+9 \int \frac {x^2}{\left (e^x+3 x\right )^2} \, dx-9 \int \frac {\log (x)}{\left (e^x+3 x\right )^2} \, dx+9 \int \frac {x \log (x)}{\left (e^x+3 x\right )^2} \, dx+588 \int \frac {1}{e^x+3 x} \, dx+1755 \int \frac {1}{\left (e^x+3 x\right )^2} \, dx-1755 \int \frac {x}{\left (e^x+3 x\right )^2} \, dx-(3 \log (x)) \int \frac {1}{e^x+3 x} \, dx\\ &=3 \int \frac {1}{x \left (e^x+3 x\right )} \, dx-3 \int \frac {x}{e^x+3 x} \, dx+3 \int \frac {\int \frac {1}{e^x+3 x} \, dx}{x} \, dx-9 \int \frac {x}{\left (e^x+3 x\right )^2} \, dx+9 \int \frac {x^2}{\left (e^x+3 x\right )^2} \, dx+9 \int \frac {\int \frac {1}{\left (e^x+3 x\right )^2} \, dx}{x} \, dx-9 \int \frac {\int \frac {x}{\left (e^x+3 x\right )^2} \, dx}{x} \, dx+588 \int \frac {1}{e^x+3 x} \, dx+1755 \int \frac {1}{\left (e^x+3 x\right )^2} \, dx-1755 \int \frac {x}{\left (e^x+3 x\right )^2} \, dx-(3 \log (x)) \int \frac {1}{e^x+3 x} \, dx-(9 \log (x)) \int \frac {1}{\left (e^x+3 x\right )^2} \, dx+(9 \log (x)) \int \frac {x}{\left (e^x+3 x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.26, size = 16, normalized size = 0.94 \begin {gather*} \frac {3 (-195+x+\log (x))}{e^x+3 x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.49, size = 15, normalized size = 0.88 \begin {gather*} \frac {3 \, {\left (x + \log \relax (x) - 195\right )}}{3 \, x + e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.88 \begin {gather*} \frac {3 \, {\left (x + \log \relax (x) - 195\right )}}{3 \, x + e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 1.59
method | result | size |
risch | \(\frac {3 \ln \relax (x )}{3 x +{\mathrm e}^{x}}+\frac {3 x -585}{3 x +{\mathrm e}^{x}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 15, normalized size = 0.88 \begin {gather*} \frac {3 \, {\left (x + \log \relax (x) - 195\right )}}{3 \, x + e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.26, size = 15, normalized size = 0.88 \begin {gather*} \frac {3\,\left (x+\ln \relax (x)-195\right )}{3\,x+{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 15, normalized size = 0.88 \begin {gather*} \frac {3 x + 3 \log {\relax (x )} - 585}{3 x + e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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