$\"\"$

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The integral is $\"\"$ .

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The integral is $\"\"$ can have three cases.

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They are $\"\"$ , $\"\"$ is negative, and $\"\"$ is positive.

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Case 1 :

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Evaluate the integral $\"\"$ for $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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$\"\"$

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Thus, $\"\"$ .

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$\"\"$

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Case 2 :

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Evaluate the integral $\"\"$ for $\"\"$ , where $\"\"$ is some constant.

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If $\"\"$ , then $\"\"$ .

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$\"\"$ .

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Consider $\"\"$ .

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Partial fraction decomposition.

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$\"\"$

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Compare coefficients of $\"\"$ terms on both sides.

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$\"\"$

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Compare constant terms on both sides.

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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If $\"\"$ , then $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Case 3 :

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Evaluate the integral $\"\"$ for $\"\"$ , where $\"\"$ is some constant.

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If $\"\"$ , then $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .