$\"\"$

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The integral is $\"\"$ .

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Rewrite the integral.

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$\"\"$ .

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$\"\"$ .

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The series is in the form of $\"\"$ .

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The power series form of $\"\"$ is $\"\"$ .

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The power series form of $\"\"$ .

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$\"\"$ .

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Apply integral on each side.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The series is $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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

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$\"\"$

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The series is converges for $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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The radius of convergence is $\"\"$ . $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The function is $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Therefore, $\"\"$ .

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$\"\"$

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$\"\"$ .