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Integrals

Question

Wired Faculty App

Evaluate: $\int \frac{\log x}{x} dx$

Solution

$I = \int \frac{\log x}{x} dx$

Substituting log x = t

Differentiating w.r.t. x, we get

$\frac{1}{x} d x = d t$

On substitution, we get

$I = \int \frac{\log x}{x} dx = \int t . dt = \frac{t^{2}}{2} + C = \frac{{(\log x)}^{2}}{2} + C$

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