Question

integral of (sin (1-x) (2-cos(1-x))^4 dx

Answer 1

Let u = 2 - (cos (1-x)).
Then du = -sin (1 - x)dx.

Go from there. You'll be integrating -u^4 du

Answer 2

This is called a u-substitution.

Answer 3

why is du=-sin (1-x)dx? I thought since subtracting the cos, and derivative of cos is -sin, that sin would be positive?

Answer 4

yeah, du=sin(1-x)

Answer 5

if you differentiate u, you get - ( - sin (1 - x) ) * (-1).
The last (-1) comes from chain rule.

Answer 6

so the last (-1) is from derivative of (1-x)?

Answer 7

To answer for verifry, yes it is.