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### Assignment 5

Calculate:

### Solution

It is clear that this integral converges, because the function is greater than from some value of . The integral of the first function yields a finite result (converges) and this will be the case with the second function. See the graph of in the figure.

The integral has a finite value.

We first look at the calculation of the indefinite integral and use integration by parts:

It seems that this has not helped us a lot, but by applying integration by parts again we get the following result:

Verify this result by differentiation.

Now we get:

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