Problems on Techniques of Integration

Use the Integration by Parts. Set

$$\left\{\begin{array}{lll} u &=& \ln(x)\\ dv &=& dx\;. \end{array}\right.$$

Then

$$\left\{\begin{array}{lll} du &=&\displaystyle \frac{1}{x} dx\\ v &=& x\;. \end{array}\right.$$

So

$$\int \ln(x) dx = x \ln(x) - \int x \frac{1}{x} dx = x \ln(x) - \int dx$$

or

$$\int \ln(x) dx = x \ln(x) - x + C\;.$$

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