[Math] Which formula do I use to integrate $ \int {\sqrt{x^2 + 81} \over 2} \,dx $

Question

I am having trouble with a question really need help please.

$$
\int {\sqrt{x^2 + 81} \over 2} \,dx
$$

I thought about taking the square root off and turning the question into $\frac 12 \int (x^2 +81)^{1/2}\, dx$ but then wondered if I could use the quotient rule.

Answer 1

Hint: Put $x = 9 \tan{t}$, then $x^{2}+81 = 81(\tan^{2}(t)+1) = 81 \cdot \sec^{2}(t)$.