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 .

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Subtitute , , and in the partial decomposed function.

Integrate on both sides.

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Consider.

Find the integral by completing the squares.

Apply integral formula : .

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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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