integral of 4/sqrt(x^2)

$$\int {\frac{ 4 }{ \sqrt{ x^2 }
} \ dx } =4*\int { \frac{ 1 }{ x } \ dx }\\
we \ substitute \ x=e^u \ then \ \ dx=e^u \ du\\
we \ have \ 4* \int { \frac{ e^u }{ e^u } \ du }=4*\int{ \ du }=4*u\\
u=\ln{ x} \\
solution: \ \ 4*\ln{ (x)}+c$$

 

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