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Recently I studied trigonometric substitution way to solve many forms of Integrals. But since I'm new at this I can't get the intuition when to use what. When it goes out of normal "formulas" , I am really lost.

For example,

dx

S(----------- )

x^2*sqrt(x^2+1)

I solved it, but had to use too many formulas for sinarctanx and cosarctgx (which are almost exact). anyway, At first I substituted x=tant, and later on I got:

S sin^-2(t)*cos(t)dt

and therefore i had to substitute z=sint

and in the end what I got is -1/sinarctgx+C.

(I checked it, if we will check what d(-1/sinarctanx) is equal to, you will get the original question, therefore its right)

And that's NOT A BEAUTIFUL FORM :(.

If can someone suggest something better out of his experience, Ill appreciate it.

Thanks in advance,

Aviv

But the way, I realized I can't copy from math-type to here (as expected, but that was my only guess).

Can someone tell me how write the function in more proper way?

Thanks

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# Trigonomatric substitutions

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