Evaluate : ∫ 1/(x(1+logx))dx\(\int\frac{1}{x(1+log\,x)}\) dx

1.	Evaluate : ∫ 1/(x(1+logx))dx\(\int\frac{1}{x(1+log\,x)}\) dx
Answer» Given, ∫ 1/(x(1+logx))dx Let 1+log x = t ⇒ \(\frac{d}{dx}\) (1 + logx) = dt ⇒ \(\frac{1}{x}\) dx = dt = \(\int\frac{1}{t}\) dt = logt +c = log (1+logx)+c

Answer»

Given,

∫ 1/(x(1+logx))dx

Let 1+log x = t

⇒ \(\frac{d}{dx}\) (1 + logx) = dt

⇒ \(\frac{1}{x}\) dx = dt

= \(\int\frac{1}{t}\) dt

= logt +c

= log (1+logx)+c

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