i486 SUPPLEMENT TO CHAP. XIV. [CHAP. n. 



Here, as before, we shall leave the discussion, as we have already all the 

 equations of which we shall make use. 



7. Integrals used in the above Discussion. For convenience 

 of reference, we here group together the known integrals employed in the 

 preceding discussion. 



/ sin x dx = cos x t I coaxdx = sina*. 

 / sin* a?d* = i isinascosoj, / cos* xdx = $x + i sin x cos x. 



I sin x cos xdx = i sin* x. 



I Bin'xdx = } cos x (2 + sin* x), I costxdx = Jsinaj(2 -f cos**). 

 / sin* xcosxdx = $sin s aj, / sina;cos*a?da>= J cos* x. 

 I XB\axdx = siax xcosx, I x cos x d x = cos x + x sin & 

 / assin 2 xdx = i* + isin*aj -J x sin x cos x. 

 I x cos* xdx = J x* i sin* x + -J x sin * cos a*. 

 / xBwxcosxdx = i(2xB\n* xx + sin a? cos a). 



