$\"\"$

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The definite integral is $\"\"$ .

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The degree of numerator is equal to the degree of denominator, hence perform the long division.

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$\"\"$

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The expression can be written as follows. \ \

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$\"\"$

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Apply partial fraction decomposition.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Equate coefficients of $\"\"$ terms.

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$\"\"$

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Equate coefficients of $\"\"$ terms.

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$\"\"$

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Equate constant terms.

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$\"\"$

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Substitute $\"\"$ in equation (3).

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$\"\"$

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Substitute $\"\"$ in equation (2).

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$\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in equation (1).

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$\"\"$

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Consider $\"\"$ then $\"\"$ .

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Substitute corresponding values in above equation.

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$\"\"$

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Substitute $\"\"$ in above equation.

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .