Evaluate the following integrals :\(\int\)\(\frac{1}{x(3+log\,x)}\)dx

1.	Evaluate the following integrals :\(\int\)\(\frac{1}{x(3+log\,x)}\)dx
Answer» Assume, 3 + logx = t d(3 + logx) = dt ⇒ \(\frac{1}{x}\)dx = dt Put t and dt in given equation we get, ⇒ ∫\(\frac{dt}{t}\) = ln\|t\| + c. But, t = 3 + logx = ln\|3 + logx\| + c

Answer»

Assume,

3 + logx = t

d(3 + logx) = dt

⇒ \(\frac{1}{x}\)dx = dt

Put t and dt in given equation we get,

⇒ ∫\(\frac{dt}{t}\)

= ln|t| + c.

But,

t = 3 + logx

= ln|3 + logx| + c

Discussion