Integrand size = 14, antiderivative size = 7 \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=16 (4+x) \log (x) \]
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Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.43, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {14, 45, 2332} \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=16 x \log (x)+64 \log (x) \]
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Rule 14
Rule 45
Rule 2332
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {16 (4+x)}{x}+16 \log (x)\right ) \, dx \\ & = 16 \int \frac {4+x}{x} \, dx+16 \int \log (x) \, dx \\ & = -16 x+16 x \log (x)+16 \int \left (1+\frac {4}{x}\right ) \, dx \\ & = 64 \log (x)+16 x \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.43 \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=64 \log (x)+16 x \log (x) \]
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Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.57
method | result | size |
default | \(16 x \ln \left (x \right )+64 \ln \left (x \right )\) | \(11\) |
norman | \(16 x \ln \left (x \right )+64 \ln \left (x \right )\) | \(11\) |
risch | \(16 x \ln \left (x \right )+64 \ln \left (x \right )\) | \(11\) |
parallelrisch | \(16 x \ln \left (x \right )+64 \ln \left (x \right )\) | \(11\) |
parts | \(16 x \ln \left (x \right )+64 \ln \left (x \right )\) | \(11\) |
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none
Time = 0.36 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=16 \, {\left (x + 4\right )} \log \left (x\right ) \]
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Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.43 \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=16 x \log {\left (x \right )} + 64 \log {\left (x \right )} \]
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none
Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.43 \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=16 \, x \log \left (x\right ) + 64 \, \log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.43 \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=16 \, x \log \left (x\right ) + 64 \, \log \left (x\right ) \]
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Time = 12.93 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int \frac {64+16 x+16 x \log (x)}{x} \, dx=16\,\ln \left (x\right )\,\left (x+4\right ) \]
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