To find the integral of the given expression, we can break it down into individual integrals:
∫(1/(x - 1) + 1/16 + 1/(x + 5) + 3/(4) + 1/(x + 5)^2) dx
= ∫(1/(x - 1)) dx + ∫(1/16) dx + ∫(1/(x + 5)) dx + ∫(3/4) dx + ∫(1/(x + 5)^2) dx
Now, let's integrate each term separately:
1. ∫(1/(x - 1)) dx = ln|x - 1| + C1
2. ∫(1/16) dx = (1/16)x + C2
3. ∫(1/(x + 5)) dx = ln|x + 5| + C3
4. ∫(3/4) dx = (3/4)x + C4
5. ∫(1/(x + 5)^2) dx = -1/(x + 5) + C5
Where C1, C2, C3, C4, and C5 are constants of integration.
So, the integral of the given expression is:
ln|x - 1| + (1/16)x + ln|x + 5| + (3/4)x - 1/(x + 5) + C
