134 
MEMORIAS CIENTmCAS I LITERARIAS 
VIII. n es negative: 
/ 
sen m x d x 
cos n x 
senm— 1 x 
m — 1 r senm— 2xdx 
(m — n) cos 11 1 x m — n J cos n x 
IX. Cambiando n per — m, 
[ tgm xdx = -“-i-™ tgm— 1 x — f tgm — 2 x d X 
J ° m — 1 J ° 
X. m==2, n=0: 
/ 
sen 2 x d x==— -i- (sen x cos x — x 
XI 
• /■ 
dx 
COS X 1 
X 
sen 3 x 
2 sen 2 x 2 ^ 2 
XII. 
/ 
sen 4 x 
cosx 
sen x 
dx= - “;-”(sen 2 x +■ 3) + L U 
■f± ~ 1 X- 
i. 4 x 2 I 
XIII. f sen 3 x cos 3 X di = cos 3 x ^ sen 3 x + -~^ 
XIV. 
J apn v 
dx 
sen x cos 4 x 3 cos 3 x cos x 
1 1 T 1 
+ + L tg — x 
r 
XV. J tg 4 x d x = - 5 -tg®x — tgx-fx. 
5. /-x D cosxdx. u = x n . •. du = ux n “ 1 dx 
d v — cos x d x 
v = sen x 
