Integrand size = 5, antiderivative size = 8 \[ \int \frac {10}{x} \, dx=8+5 \log \left (x^2\right ) \]
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Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 29} \[ \int \frac {10}{x} \, dx=10 \log (x) \]
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Rule 12
Rule 29
Rubi steps \begin{align*} \text {integral}& = 10 \int \frac {1}{x} \, dx \\ & = 10 \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.50 \[ \int \frac {10}{x} \, dx=10 \log (x) \]
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Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62
method | result | size |
default | \(10 \ln \left (x \right )\) | \(5\) |
norman | \(10 \ln \left (x \right )\) | \(5\) |
risch | \(10 \ln \left (x \right )\) | \(5\) |
parallelrisch | \(10 \ln \left (x \right )\) | \(5\) |
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none
Time = 0.23 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.50 \[ \int \frac {10}{x} \, dx=10 \, \log \left (x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.38 \[ \int \frac {10}{x} \, dx=10 \log {\left (x \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.50 \[ \int \frac {10}{x} \, dx=10 \, \log \left (x\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int \frac {10}{x} \, dx=10 \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.50 \[ \int \frac {10}{x} \, dx=10\,\ln \left (x\right ) \]
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