Answer: ln|y/8| + C
Explanation:
First, we need to recognize that the derivative of arctan(x) is 1/(1+x^2). Therefore, the derivative of arctan(y/8) is 8/(64+y^2).
Now, using the substitution u = y/8, we can rewrite the integral as:
∫(1/u)(64+64u^2)(8/(64+64u^2))du
Simplifying, we get:
∫(1/u)du = ln|u| = ln|y/8|
Therefore, the final answer is:
ln|y/8| + C
where C is the constant of integration.