Question

Find the following integrals:(i) `int(sinx+cosx)dx` (ii) `intcosecx(cosecx+cosx)dx`(iii) `int(1-sinx)/(cos^2x)dx`

Answer 1

(i) `int(sinx+cosx)dx = -cosx+sinx+c`

(ii)`int cosecx(cosecx+cotx)dx`
`=int cosec^2x dx+ int cosecxcotxdx`
`= - cotx+(-cosecx)+c`
`= - cotx-cosecx+c`
(iii) `int (1-sinx)/cos^2xdx`
`= int (1/cos^2x - sinx/cos^2x) dx`
`= int sec^2x dx - int tanxsecx dx`
`= tanx-secx+c`