1.

Evaluate the following integrals :\(\int\frac{log\,x}{x}\)dx

Answer»

Assume,

logx = t 

⇒ d(logx) = dt 

⇒ \(\frac{1}{x}\)dx = dt

Substituting t and dt in above equation we get,

⇒ \(\int\)t.dt

⇒ \(\frac{t^2}{2}+c\)

But,

t = log(x) 

⇒ \(\frac{log^2x}{2}\) + c  .



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