Question

Find ∫ f(x) = x − 16 sin(2x).

Answer 1

The integral of the function f(x) = x - 16 sin(2x) is ½ x² - 8 cos(2x) + C, where C is the constant of integration.

Step-by-step explanation:

The student asked to find ∫ f(x) = x − 16 sin(2x). To solve this, we apply the rules of integration to each term separately. The integral of x with respect to x is ½ x², following the power rule of integration. For the second term, integrating −16 sin(2x) involves using the substitution method or recognizing that it is a standard integral, resulting in − 8 cos(2x). Therefore, the antiderivative of f(x) is ½ x² - 8 cos(2x) plus a constant of integration, commonly denoted as C.