Question

Integral of y/((y^2)-1)

Answer 1

The integral of y/((y^2)-1) is (1/2) ln|y^2 - 1| + C.

Step-by-step explanation:

To evaluate the integral of y/((y^2)-1), we can perform a substitution by letting u = y^2 - 1. Then, du = 2y dy, and the integral becomes:

∫ y/((y^2)-1) dy = (1/2) ∫ 1/u du = (1/2) ln|u| + C

Substituting back u = y^2 - 1, the final answer is (1/2) ln|y^2 - 1| + C.

Answer 2

Hint:
`\frac y{y^2-1}=\frac y{(y+1)(y-1)}=\frac12\left(\frac1{y+1}+\frac1{y-1}\right)`