Integrand size = 12, antiderivative size = 17 \[ \int \frac {40+5 x}{24 x} \, dx=-2+\frac {5 x}{24}+\frac {5}{3} \log \left (\frac {x}{3}\right ) \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.71, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 45} \[ \int \frac {40+5 x}{24 x} \, dx=\frac {5 x}{24}+\frac {5 \log (x)}{3} \]
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Rule 12
Rule 45
Rubi steps \begin{align*} \text {integral}& = \frac {1}{24} \int \frac {40+5 x}{x} \, dx \\ & = \frac {1}{24} \int \left (5+\frac {40}{x}\right ) \, dx \\ & = \frac {5 x}{24}+\frac {5 \log (x)}{3} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \frac {40+5 x}{24 x} \, dx=\frac {5}{24} (x+8 \log (x)) \]
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Time = 0.01 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.53
method | result | size |
default | \(\frac {5 x}{24}+\frac {5 \ln \left (x \right )}{3}\) | \(9\) |
norman | \(\frac {5 x}{24}+\frac {5 \ln \left (x \right )}{3}\) | \(9\) |
risch | \(\frac {5 x}{24}+\frac {5 \ln \left (x \right )}{3}\) | \(9\) |
parallelrisch | \(\frac {5 x}{24}+\frac {5 \ln \left (x \right )}{3}\) | \(9\) |
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none
Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {40+5 x}{24 x} \, dx=\frac {5}{24} \, x + \frac {5}{3} \, \log \left (x\right ) \]
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Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.59 \[ \int \frac {40+5 x}{24 x} \, dx=\frac {5 x}{24} + \frac {5 \log {\left (x \right )}}{3} \]
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none
Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {40+5 x}{24 x} \, dx=\frac {5}{24} \, x + \frac {5}{3} \, \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.53 \[ \int \frac {40+5 x}{24 x} \, dx=\frac {5}{24} \, x + \frac {5}{3} \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.47 \[ \int \frac {40+5 x}{24 x} \, dx=\frac {5\,x}{24}+\frac {5\,\ln \left (x\right )}{3} \]
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