CHAPTER XII 



97. The work of this chapter is devoted to some of the different 

 methods involved in the integration of well-known trigono- 

 metrical functions. 



f fsm x 



(a) Itan x dx = \ 



J J cos 



--J- 



dx 

 v 



sin x dx 



(b) Icot x dx = 



COS X 



- log e cos x 

 Iog 8 sec x 



cos x dx 

 sin x 



log e sin x 



(c) |cosec x dx = \-. 



J Jsina? 



i 



dx 



X X 



2 sin - cos - 



Psec 2 - dx 



2 I . ~ 



J tan- 



t 



on dividing numerator and denominator by cos 2 -. 







>vi fin 



Put y = tan ~. Then dy = - sec 2 - dx 



2 i ft 



and Icosec x dx = I 



J Jy 



tan 



173 



