The integral is .

Find the integral using integration by parts.

Integration by parts formula: .

Let and .

Find by integrating .

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Differentiate on each side.

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Substitute ,  and in integration by parts formula.

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Consider the antiderivative function by taking as  .

Graph the integrand function and its antiderivative .

Observe the graph,

When is negative, then is decreasing and is positive , then is increasing.

Hence the curve is derivative of the curve .

Therefore, is antiderivative of the integrand function .

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