Question

Make a substitution to express the integrand as a rational function and then evaluate the integral.

Integrate[sqrt x/(x-36), {x, 4, 9}]

Answer 1

\[\int\limits_{4}^{9} \sqrt x/(x-36) dx\]

Answer 2

Substitute \(u=\sqrt{x} \implies x=u^2 \implies dx=2udu \) to get
\[\int_4^9 \frac{u}{u^2-36}2udu=2\int_4^9 \frac{u^2}{u^2-36}du=\cdots\]
Can you take it from here?