$\"\"$

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The integral expression is $\"\"$ .

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Using theorem :

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If $\"\"$ is integrable on $\"\"$ , then $\"\"$ .

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Where $\"\"$ .

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The integral expression is $\"\"$ .

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Here $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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

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$\"\"$ .

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$\"\"$

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$\"\"$

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Since $\"\"$

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$\"\"$

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$\"\"$

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Sum of first $\"\"$ natural numbers is $\"\"$ .

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Sum of the squares of first $\"\"$ natural numbers is $\"\"$ .

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Sum of the cubes of first $\"\"$ natural numbers is $\"\"$ .

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Simplify the expression.

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$\"\"$

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$\"\"$ . $\"\"$

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$\"\"$ .