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# Calculus Challenge Watch

1. Let's see who's got the brain to solve this problem.
Compute the integral

where the expression in the integrand contains square roots.
2. (Original post by Omio)
Let's see who's got the brain to solve this problem.
THe integral may be written form bellow

And can be solved with series of substitution
First:
a=x+2 and dx=da
so

now substitute
b=Va ->a=b^2 ->da=2b db so

substitute
-> b=c^2-2 ->db=2c dc
so

and continue with similar substitution up to there is not sqare root.
You will for example substituting n-times (n square root) and at last with z

Then multplying the powers integrate by terms and resubstitute.
It means long and systematic work.
For an example:
http://www.wolframalpha.com/input/?i...29%29%29%29+dx
3. (Original post by Omio)
Let's see who's got the brain to solve this problem.
It would be better, If you post this in here
4. see if you can get an ODE out of that by differentiating and squaring

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