- #1
mattmannmf
- 172
- 0
Using U-substitution find the indefinite integral of:
[sin(2x)/cos^4(2x)] dx
So I do know that it will have to come out to it being ln... here's what i did so far
ok so i made u= cos^4(2x)
du= -8cos^3(2x)*sin(2x)dx...(just took the derivative of u and simplified it)
so made sin(2x)dx= du/(-8cos^3(2x))...so i can substitute it into my equation.
so it came out to be:
du/(u*-8cos^3(2x))...but in using u-substitution, i should not have an x variable...
So do i have to minipulate u=cos^4(2x) to get x by its self?
I get x= .5cos^-1(4sqrt(x))
It just seems like its sooooo complicated.. don't know.
[sin(2x)/cos^4(2x)] dx
So I do know that it will have to come out to it being ln... here's what i did so far
ok so i made u= cos^4(2x)
du= -8cos^3(2x)*sin(2x)dx...(just took the derivative of u and simplified it)
so made sin(2x)dx= du/(-8cos^3(2x))...so i can substitute it into my equation.
so it came out to be:
du/(u*-8cos^3(2x))...but in using u-substitution, i should not have an x variable...
So do i have to minipulate u=cos^4(2x) to get x by its self?
I get x= .5cos^-1(4sqrt(x))
It just seems like its sooooo complicated.. don't know.