The integral is .

Consider integrand function .

Partial fraction decomposition.

Equate coefficients of like terms on each side.

Solve the above system of equations.

Substitute  in equation .

Substitute  and  in equation .

Substitute  in equation .

Subtitute , ,  and  in the partial decomposed function.

Integrate on both sides.

.

Consider.

Find the integral by completing the squares.

Apply integral formula : .

.

Consider .

Let , then

Differentiate on each side.

Substitute ,  and  in the integral.

Consider .

Let .

If , then .

Differentiate on each side.

Substitute  and  in the integral.

Again consider , then 

Substitute  in the above integral.

If  then .

Replace  in above expression.

Replace  in above expression.

Substitute above result in .

Replace  in above expression.

Therefore,

.

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