Find the integral of ∫1/(1+tanx)dx

[Rhdjfgjgj]

Homework Statement

my teacher told me to solve this one in all the possible ways . I seem to have missed out on any one of them. Please help me oout

Relevant Equations

All standard integrals and concepts covered in AP calculus

I have done one by assuming tanx as u in substitution

 

[bob012345]

Homework Statement: my teacher told me to solve this one in all the possible ways . I seem to have missed out on any one of them. Please help me oout
Relevant Equations: All standard integrals and concepts covered in AP calculus

I have done one by assuming tanx as u in substitution

Please show us. Thanks.

 

[dextercioby]

What is all possible ways? I can think of only substitution, but not the one you attempted. I think a half-angle should be better.

 

[pasmith]

Also consider $$\tan(x - a) = \frac{\tan x - \tan a}{1 + \tan x \tan a}<br /> = \frac{1}{\tan a} - \left(\frac{1}{\tan a} + \tan a\right) \frac{1}{1 + \tan x \tan a}$$ for suitable $a$.