Integrand size = 5, antiderivative size = 14 \[ \int \frac {4}{x} \, dx=-3-\log \left (\frac {16 \log ^2(3)}{x^4}\right ) \]
[Out]
Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 29} \[ \int \frac {4}{x} \, dx=4 \log (x) \]
[In]
[Out]
Rule 12
Rule 29
Rubi steps \begin{align*} \text {integral}& = 4 \int \frac {1}{x} \, dx \\ & = 4 \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int \frac {4}{x} \, dx=4 \log (x) \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36
method | result | size |
default | \(4 \ln \left (x \right )\) | \(5\) |
norman | \(4 \ln \left (x \right )\) | \(5\) |
risch | \(4 \ln \left (x \right )\) | \(5\) |
parallelrisch | \(4 \ln \left (x \right )\) | \(5\) |
[In]
[Out]
none
Time = 0.24 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int \frac {4}{x} \, dx=4 \, \log \left (x\right ) \]
[In]
[Out]
Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.21 \[ \int \frac {4}{x} \, dx=4 \log {\left (x \right )} \]
[In]
[Out]
none
Time = 0.21 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int \frac {4}{x} \, dx=4 \, \log \left (x\right ) \]
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int \frac {4}{x} \, dx=4 \, \log \left ({\left | x \right |}\right ) \]
[In]
[Out]
Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.29 \[ \int \frac {4}{x} \, dx=4\,\ln \left (x\right ) \]
[In]
[Out]