Question

integration using u sub of cos^2(sinx)cosx

Answer 1

did you try
u = sin x
?

Answer 2

yup

Answer 3

where are you stuck ?
du = .. ?

Answer 4

du=cosxdx, dx=du/cosx

Answer 5

correct, go on

Answer 6

used the trig identity that cos^2(u)= 1+cos(2u)/2

Answer 7

canceled one of the cosx with the added du/cosx

Answer 8

and got 1/2(1+cos(2u)

Answer 9

and you still need to integrate that, isn't it ?
with respect to 'u'

Answer 10

and bdw, thats correct till there

Answer 11

i am sure you know the integration of 1
are u stuck at finding integration of cos 2u ?

Answer 12

no derived with repect to x cuz i came up with 1/2(x + sin(2u)/2+c, but should have been 1/2(du+sin(2sin(x)/2)

Answer 13

1/2(u+ sin(2u)/2+c

Answer 14

u/2 + (sin 2u)/4 + c

now plug back in
u = sin x

Answer 15

\(\Large \int 1 du =u+c\)

Answer 16

yup got it from there, thanks for the help bud

Answer 17

welcome :)