Question

integral of 6cos^4x

Answer 1

cos^2x=1/2[1+\cos(2x)]
apply multiple times

Answer 2

damn latex...

Answer 3

cos^2(x)=1/2+1/2cos(2x)

Answer 4

...or use a reduction formula if that floats your boat

Answer 5

id prefer breaking it up and using half angle

Answer 6

then do it twice and integrate

Answer 7

there is better way , split up cos^4x = cos^2x * cos^2x
now rewrite the second cos^2x as (1-sin^2 x)
rewrite it as cos^2x - cos^2x sin^2x,
rewrite this using double angle formulae

Answer 8

how would you integrate the second term @psi9epsilon ?

Answer 9

good question
remember sin2x= 2 sinxcosx, so sin^2(2x)= 4 cos^2(x_)sin^2(x), remove the 4 from write side and write the right side of eqn as sin^2(2x)/4 and thats easy to integrate

Answer 10

nice