Let me just retype what you have so others can read it easier:
Substitue
Is this where you are stuck?
Try to do integration by parts.
Hello guys here is my problem uploaded: , see the attached image of my scanned paper
The thing that i wonder about here is the hint : 2$cos u * u * dx-
Where this this expression come from, how did they apply Cos to .where did it suddenly come from. I can understand why the constant was suddenly omitted from the right side of the equation (Constant Multiplie Rule). Would be happy if someone could solve this for me.
Snowteas and prove its ways of solving are different, Snowtea you based your on my variable substitution by using u^2.
Prove it could you elaborate on your expression of getting to: \displaystyle \int{\cos{\sqrt{x}}\,dx} = \int{\frac{2\sqrt{x}\cos{\sqrt{x}}}{2\sqrt{x}}\,dx } because all I can understand now after looking at the derivate of sqrt[x] is that the derivate is given by using "Difference of two squares" formula and then you get 1/2*sqrt[x]. Thats understandable after trying it out myself half an hour ago.
Also both of your answers lead to the same integral, here is where i am stuck again.
I have integrated by using the DI shorcut (http://www.delmar.edu/math/MLC/Forms...By%20Parts.pdf) for fast results now.
Here is my solution Tell me if it's appropriate or not.