Question

How do you find the integral of `int 1/(1 + csc(x))`?

Answer 1

`x+secx-tanx+c`

Explanation:

`int1/(1+cscx)dx=intsinx/(1+sinx)dx=int(sinx-sin^2x)/(cos^2x)dx`
=`inttanxsecxdx-inttan^2xdx`
=`inttanxsecxdx-int (sec^2x-1)dx`
=`secx-(tanx-x)+c`
=`x+secx-tanx+c`