Integrand size = 17, antiderivative size = 13 \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx=1+\frac {3 x}{2}+\log ^2\left (x^2\right ) \]
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Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.176, Rules used = {12, 14, 2338} \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx=\log ^2\left (x^2\right )+\frac {3 x}{2} \]
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Rule 12
Rule 14
Rule 2338
Rubi steps \begin{align*} \text {integral}& = \frac {1}{2} \int \frac {3 x+8 \log \left (x^2\right )}{x} \, dx \\ & = \frac {1}{2} \int \left (3+\frac {8 \log \left (x^2\right )}{x}\right ) \, dx \\ & = \frac {3 x}{2}+4 \int \frac {\log \left (x^2\right )}{x} \, dx \\ & = \frac {3 x}{2}+\log ^2\left (x^2\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx=\frac {3 x}{2}+\log ^2\left (x^2\right ) \]
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Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85
method | result | size |
default | \(\frac {3 x}{2}+\ln \left (x^{2}\right )^{2}\) | \(11\) |
norman | \(\frac {3 x}{2}+\ln \left (x^{2}\right )^{2}\) | \(11\) |
risch | \(\frac {3 x}{2}+\ln \left (x^{2}\right )^{2}\) | \(11\) |
parts | \(\frac {3 x}{2}+\ln \left (x^{2}\right )^{2}\) | \(11\) |
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none
Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx=\log \left (x^{2}\right )^{2} + \frac {3}{2} \, x \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx=\frac {3 x}{2} + \log {\left (x^{2} \right )}^{2} \]
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none
Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx=\log \left (x^{2}\right )^{2} + \frac {3}{2} \, x \]
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx=\log \left (x^{2}\right )^{2} + \frac {3}{2} \, x \]
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Time = 8.94 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.77 \[ \int \frac {3 x+8 \log \left (x^2\right )}{2 x} \, dx={\ln \left (x^2\right )}^2+\frac {3\,x}{2} \]
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