integrate:cos^10xdx

Question

even with the previous hint a tutor here gave me i still don,t know it

Answer 1

hmmm lets see
using demovire theorm
z+1/z=2cosx and z^n+1/z^n=2cosnx
in our case
2cosx=(z+1/z)
pascal triangle
(z+1/z)^10
from left to right are
1,10,45,120,210,252,210,120,45,10 and 1
the coeffient now 1st,2nd---last
1st term:z^10
2ndterm:10z^9(1/z)=10z^8
3rdterm:45z^8(1/z)^2=45z^6
4thterm:120z^7(1/z)^3=120z^4
5thterm:210z^6(1/z)^2=210z^2
6thterm:252z^5(1/z)^5=252
7thterm:210z^4(1/z)^6=210/z^2
8thterm:120z^3(1/7)^7=120/z^4
9thterm:45z^2(1/z)^8=45/z^6
10thterm:10z(1/z)^9=10/z^8
11term:1/z^10
then
z^10+10z^8+45z^6+120z^4+210z^2+252+120/z^2+120/z^4+45/z^6+10/z^8+1/z^10
arrange them
z^10+1/z^10+10z^8+10/z^8+45z^6+45/z^6+120/z^4+120/z^4+210z^2+210/z^2+252
factor out
(z^10+1/z^10)+10(z^8+1/z^8)+45(z^6+1/z^6)+120(z^4+1/z^4)+210(z^2+1/z^2)+252
recap
z^n+1/z^n=2cosx
2cos10x+20cos8x+90cos6x+240cos4x+420cos2x+252
1024cos^10x=2cos10x+20cos8x+90cos6x+240cos4x+420cos2x+252
now divide by 1024
1/512cos10x+5/256cos8x+45/512cos8x+15/64cos4x+105/256cos2x+63/256
now just integrate them term by term
i need a big thanks

Answer 2

thank you very much sir collins

Answer 3

you are welcome read out calculus made easy on schaum's outline these book was recommende to me by my favorite tutor here STEVE...that book is a life saving one if you can not get one locally use amazon..steve favorite statement
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try it out