Chapter 9.4, Problem 13E

To determine

To find: the value of improper integral.

Answer to Problem 13E

The value of integral is $\ln 2$ .

Explanation of Solution

Given information:

The improper integral is ${\displaystyle {\int }_{-1}^{\infty }\frac{1}{x^2+5x+6}dx}$ .

Calculation: by using definition of improper integrals with infinite integration limits, the improper integral can be written as:

  ${\displaystyle {\int }_{-1}^{\infty }\frac{1}{x^2+5x+6}dx}=\underset{a\to \infty }{\lim }{\displaystyle {\int }_{-1}^a\frac{1}{x^2+5x+6}dx}$

To find the value of integral, first integrate and then simplify,

Thus, the value is $\ln 2$ .