Question

If ∫ e^x(tanx +1)secx dx = e^x f(x) + c then write the value f(x).

Answer 1

Given,

∫ e^x(tanx +1)sec x dx

It is clearly of the form,

By comparison, 

f(x) = 1 + tanx ; 

f^I(x) = secx

= e^x (1 + tanx) + c

Therefore,

The value of f(x) = 1+ tanx