Question

x +2/√x square+ 2x + 3. dx​

Answer 1

Answer:

I'm asked to evaluate this integral: ∫x2−2x−3−−−−−−−−−√dx

I don't see any other way to solve this except by trigonometric substitution, which is precisely what I did once I completed the square and got 4−(x−1)2−−−−−−−−−−√ as the integrand.

I then performed a substitution with (x−1)=2sin(θ).

But all of the answer choices contain some natural logarithms in them. I have no clue how that's possible.

What other methods are there for solving this problem?