I have been given the problem ∫√(e(adsbygoogle = window.adsbygoogle || []).push({}); ^{x}-3)

and we must use the substitution u = √(e^{x}-3)

I can start it off with u = √(e^{x}-3)

and du = e^{x}dx/2u

and what Ive been trying is to complete the square and go towards 2 ∫ u^{2}du/((u^{2}+4) -1)

But im not getting towards the answer, either Im doing something wrong in the middle, or my approach is wrong.

the answer given is 2√(e^{x}-3) - 2 √3 arctan(e^{x}-3)/√3) +c

any help would really be appreciated, ive searched online trying to find a pattern, but i just cant figure it out

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# I Integration technique

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