Problem 33E

Simple irreducible quadratic factors

Evaluate the following integrals.

Problem 33E

Simple irreducible quadratic factors Evaluate the following integrals.

Answer

We have to evaluate the integral

Take a partial fraction

Multiply equation by denominator

Simplify

Plug in x=1 into the equation

Put this into equation (1)

Therefore

= …. (2)

Put u=x+2

Substitute back u=

…(3)

…(4)

Therefore

=

Where C is integration constant