Evaluate the following integrals : ∫tanx/(secx + tanx) dx ​

Question

Evaluate the following integrals :

\(\int\frac{tan\,x}{sec\,x+tan\,x}\)dx

Answer 1

Let I = \(\int\frac{tan\,x}{sec\,x+tan\,x}\)dx

On multiplying and dividing (sec x – tan x), we can write the integral as

∴ I = sec x – tan x + x + c

Thus,

\(\int\frac{tan\,x}{sec\,x+tan\,x}\)dx = secx - tanx + x + c