Integrand size = 53, antiderivative size = 23 \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=-\frac {1}{5}+\log \left (4 e^{\frac {e^{3 x}}{x+\log (2 x)}}\right ) \]
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Time = 0.16 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {6820, 2326} \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=\frac {e^{3 x} \left (x^2+x \log (2 x)\right )}{x (x+\log (2 x))^2} \]
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Rule 2326
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{3 x} \left (-1-x+3 x^2+3 x \log (2 x)\right )}{x (x+\log (2 x))^2} \, dx \\ & = \frac {e^{3 x} \left (x^2+x \log (2 x)\right )}{x (x+\log (2 x))^2} \\ \end{align*}
Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61 \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=\frac {e^{3 x}}{x+\log (2 x)} \]
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Time = 0.06 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61
method | result | size |
risch | \(\frac {{\mathrm e}^{3 x}}{\ln \left (2 x \right )+x}\) | \(14\) |
parallelrisch | \(\frac {{\mathrm e}^{3 x}}{\ln \left (2 x \right )+x}\) | \(14\) |
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Time = 0.25 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=\frac {e^{\left (3 \, x\right )}}{x + \log \left (2 \, x\right )} \]
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Time = 0.09 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.43 \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=\frac {e^{3 x}}{x + \log {\left (2 x \right )}} \]
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Time = 0.34 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=\frac {e^{\left (3 \, x\right )}}{x + \log \left (2\right ) + \log \left (x\right )} \]
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Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=\frac {e^{\left (3 \, x\right )}}{x + \log \left (2 \, x\right )} \]
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Time = 14.57 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.57 \[ \int \frac {e^{3 x} \left (-1-x+3 x^2\right )+3 e^{3 x} x \log (2 x)}{x^3+2 x^2 \log (2 x)+x \log ^2(2 x)} \, dx=\frac {{\mathrm {e}}^{3\,x}}{x+\ln \left (2\,x\right )} \]
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