Find the Antiderivative for the Function y = 1 / (7-3x) ^ 5

The antiderivative F (x) for the function f (x) has the following form: F (x) = ∫f (x) * dx + С, where С is a constant. In this case:

F (x) = ∫1 / (7 – 3x) ^ 5 * dx + C.

Let’s make a change of variables t = (7 – 3x), then:

dt = (-3) * dx;

dx = -1/3 * dt.

We get the integral:

∫ (-1/3) * t ^ (- 5) * dt + C = (-1/3) * (-1/4) * t ^ 4 + C = 1 / 12t ^ 4 + C.

Let’s make a reverse replacement:

F (x) = 1/12 * (7 – 3x) ^ 4 + C.