Question

Determine the antiderivative of y.

y=-7/(x +1)
use appropriate order of operations. use "^" to represent a power. do not use any extra spacing between characters.

Answer 1

The antiderivative of the function y = -7/(x + 1) is obtained through a simple substitution and integration process, resulting in F(x) = -7ln|x + 1| + C, where C is the constant of integration.

Step-by-step explanation:

To find the antiderivative of the function y = -7/(x + 1), we can recognize this as a simple rational function that can be integrated using the basic rules of integration for a function in the form of 1/u. Here, u is x + 1. So, the antiderivative F(x) is:

Step-by-Step Integration

Let u = x + 1, then du = dx.

The given function can now be written as y = -7/u.

The antiderivative of -7/u with respect to x is -7ln|u| + C, where C is the constant of integration.

Substitute u back in terms of x to get F(x) = -7ln|x + 1| + C.

This is the antiderivative of the given function y = -7/(x + 1).