Question

Determine whether the improper integral converges or diverges, and find the value of each that converges.

∫^[infinity]_-[infinity] 2x+4/x^2++4x+5 dx

Answer 1

Diverges

Explanation:

For the improper integral to converge the limit must exist, if the limit does not exist or is infinite the integral diverges;

`\int\limits^a_b {(2x+4)/x^2+4x+5} \, dx`#

Where a and be is infinity

The solution of this is infinity and therefore the integral diverges because the first expression is undefined because ∞/∞, the second term is 4·∞ which is infinity and infinity added to any number is infinity