Question

How do you find the antiderivative of `(sinx + cosx)/tanx`?

Answer 1

`sinx+ln|tan(x/2)|+cosx+C`

Explanation:

`I=int(sinx+cosx)/tanxdx=int(sinx+cosx)cosx/sinxdx`

`=intcosxdx+intcos^2x/sinxdx=sinx+int(1-sin^2x)/sinxdx`

`=sinx+int{1/sinx-sinx}dx`

`=sinx+int(cscx-sinx)dx`

`:. I=sinx+ln|tan(x/2)|+cosx+C`