$\"\"$

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The definite integral is $\"\"$ .

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Factorize the denominator.

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$\"\"$

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Here $\"\"$ contain irreducible quadratic factors.

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Therefore,

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$\"\"$

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Equate coefficients of like terms on each side.

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$\"\"$

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Solve the above system of equations.

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From $\"\"$ , $\"\"$ .

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From $\"\"$ , $\"\"$ .

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Therefore, $\"\"$ .

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From $\"\"$ , $\"\"$ .

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From $\"\"$ , $\"\"$ .

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Therefore, $\"\"$ .

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Thus, $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute the above result in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .