Evaluate the following integral

Question

integral 1 = a and b = 4 of
sinx dx/(1+cos)^2

u = cosx
du = -sinx dx

so from here I don't know if I can do:

-1 du = sinx dx
or 1/sin du = x dx

Answer 1

u = 1 + cos x
du = -sin x dx

so we have
-du/u

Answer 2

so I tried again and I got this, don't know if it's good:(I also put the wrong a and b)

integral 0 = a and b = pi/3 of
sinx dx/(1+cos)^2

u = cosx
du= -sinxdx
-1 du = sinx dx

so: integral -1 du/(1+u)^2
= 1/(u+1)

if x = 0, then u = 1
if x = pi/3, then u = 1

so 1/1+1 - 1/1+1 = 0

Is this correct?

Answer 3

-du/(u)^2

Answer 4

-du/u^2 ---> -1/u + c

Answer 5

ok Damon, so if you integrate what you have me, you get 1/u no? Because 1/u^2 = -1/u, so -1/u^2 = 1/u?

Answer 6

so
-1/(1+cos x) + c

Answer 7

Yes, you have it.

Answer 8

awesome, thanks man!

Answer 9

You are welcome.