Important intergration substitution

rs8910
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int^{0}_{t}[cos(sqrt{x}]dx can anyone tell me the solution to this question !
 
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Welcome to PF rs8910. You should note that homework is to be threaded in the homework help section, and any homework must be accompanied by reasonable evidence that you have given the question a fair shot, which means including working and where you are stuck.

I can give you some limited help though. First let try a substitution that would get rid of that square root sign, and try some method of integrating products of 2 functions.

EDIT: I see you have given \LaTeX a good shot, but you still need to learn how to use it properly. To see what something typed to form the TeX you see, just press on the image. It will also link you to a LaTeX guide.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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