Question

Question: Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine
cos4 x sin2 x

Answer: 1/16x - 1/64sin(4x) + 1/48 sin^3(2x) + C

Why is this answer wrong in my math software that I am using for school. I tried integrating the problem. Can anyone help by explaining step by step if it's possible, Please thank you?

Answer 1

i'm assuming you mean cos^4x sin^2x

Answer 2

cos^2x=(1+cos2x)/2

Answer 3

sin^2x=(1-cos2x)/2

Answer 4

((1-cos2x)/2)((1+cos2x)/2)^2

Answer 5

expand

Answer 6

1/8(1+cosx+cos^2(2x)+cos^3(2x))

Answer 7

split up the functions.

Answer 8

into \[1/8(\int\limits(1+\cos x+\cos ^{2}2x)dx+\int\limits( \cos ^{2}2x*\cos2x)dx\]

Answer 9

then u substitution.

Answer 10

u=sin2x

Answer 11

then it's easy after that.

Answer 12

i got lost after the 8th statement