Integrand size = 4, antiderivative size = 10 \[ \int \log \left (x^2\right ) \, dx=-2 x+x \log \left (x^2\right ) \]
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Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2332} \[ \int \log \left (x^2\right ) \, dx=x \log \left (x^2\right )-2 x \]
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Rule 2332
Rubi steps \begin{align*} \text {integral}& = -2 x+x \log \left (x^2\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \log \left (x^2\right ) \, dx=-2 x+x \log \left (x^2\right ) \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.10
method | result | size |
default | \(-2 x +x \ln \left (x^{2}\right )\) | \(11\) |
norman | \(-2 x +x \ln \left (x^{2}\right )\) | \(11\) |
risch | \(-2 x +x \ln \left (x^{2}\right )\) | \(11\) |
parallelrisch | \(-2 x +x \ln \left (x^{2}\right )\) | \(11\) |
parts | \(-2 x +x \ln \left (x^{2}\right )\) | \(11\) |
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \log \left (x^2\right ) \, dx=x \log \left (x^{2}\right ) - 2 \, x \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \log \left (x^2\right ) \, dx=x \log {\left (x^{2} \right )} - 2 x \]
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none
Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \log \left (x^2\right ) \, dx=x \log \left (x^{2}\right ) - 2 \, x \]
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \log \left (x^2\right ) \, dx=x \log \left (x^{2}\right ) - 2 \, x \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \log \left (x^2\right ) \, dx=x\,\left (\ln \left (x^2\right )-2\right ) \]
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