The integral is .

Algebraic formula: .

Here  contains irreducible quadratic factors.

Therefore,

Substitute  in above expression.

.

Equate coefficients of  terms on each side.

Equate coefficients of  terms on each side.

.

Substitute ,  and  in .

Apply formula: .

.

Consider .

Let .

Differentiate on each side.

.

Substitite  and  in .

Consider .

Find the integral by completing the squares.

Apply formula :.

Substitute above result in .

Substitute above result in .

.

.