Hello Prove it,
i ended up with the same thing as you. Here is my reasoning.
u = sin(x) u'=cos(x)
I must change the function in terms of u, so I start with the denominator.
Now I will change my numerator cosx, in terms of u. Using the trigonometric Identity
so now I have ....
Now I must change the constant multiplier of dx. I am going to use
Using
& du or u'=cosx, I set them equal to eachother.
NOTE: I must also change u' in terms of u
So now I have dx in terms of u,
Notice that cosx still has an x. I must remember to keep everything in terms of u. So remembering back to the trigonometric identity,
I now have
= 1
I plug that back into my new integral