Question

tanx/secx+tanx,Integrate the given function w.r.t. x considering them well defined and integrable over proper domain.

Answer 1

=tan x/ sec x. + tan x
=tan x / 1/ tan x. + tan x
= tan x squre. + tan x

Answer 2

Answer:

Secx-tanx+x+c

Step-by-step explanation:

We have to evaluate the following:

∫$\frac{tanx}{Secx +tanx} dx$

Now, ∫$\frac{tanx}{Secx +tanx} dx$

=∫$\frac{tanx(Secx-tanx)}{Sec^{2}x-tan^{2}x  } dx$

=∫$(Secx tan x-tan^{2}x) dx$ {Since we know that Sec²x- tan²x =1}

=∫$(Secx Tanx+1-Sec^{2} x) dx${ Again we have used the formula  Sec²x- tan²x =1}

= Secx +x- tanx +c (Where c is an integration constant) {Since we know that, ∫(Secx Tanx) dx =Sec x.}

=Secx-tanx+x+c (Answer)