Integral something something.

What is the derivative of \(\displaystyle \frac{-4}{\sqrt{{3+\sqrt x}}}~?\) SEE HERE
 
Hi,
Can you show us what you tried? Since it is not in a form of a integral that we know the integral of then you need to make a u-substitution, I would try letting u= sqrt(x) and if that does not work then try u=3+sqrt(x)and if that does not work then try ....
Integrals are puzzles and you just have to try different substitutions until one works.
 
I think Jomo's suggestion is the place to start; generally, you just try various substitutions and see whether they work out. Often it is not obvious what will be best.

In the case of Khan's suggestion, it looks like an extension of a trig substitution that is useful when there is something of the form a^2 + u^2, where in this case u would be the fourth root of x. The way to see why, ultimately, will be to try it and see. (My guess is that you have not seen trig substitutions yet, but you will eventually!)

Substitutions are something you learn by experience, and the way to gain that experience is to do lots of substitutions, including those you might not have thought of. Once you see one work, you will be likely to recognize future situations in which it might work.

So, give each idea a try, and show us what happens!
 
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