Evaluate the integral, and show all steps. Could someone please help me with this integral please? Thanks!

Question

Answer 1

1 / (x² - 8x + 25) = 1 / [(x² - 8x + 16) + 9] = 1 / [(x - 4)² + 9]

So, we have 50∫ (1 / [(x-4)² + 9])dx = (50/9) ∫ (1 / [((x-4)/3)² + 1])dx

Let u = (x-4)/3. Then du = (1/3)dx. So, dx = 3du.

We then have (50/3) ∫ [1 / (1 + u²)]du = (50/3)Arctanu + C = (50/3)Arctan [(x-4)/3] + C