## Problems on Techniques of Integration

The exponential function is a nice function since its derivative and antiderivative are the same. So for the integration by parts, this function has the same behavior whether we differentiate it or take its antiderivative. Therefore the focus should be on the other function involved in the integration. In this case, we must differentiate because its derivative will lower its degree.

Set

Then

Since

we get

In order to integrate the function , we will need to do another integration by parts. This is very common that an integration by parts may lead to another one or may be more integration by parts. Set

Then

Since

we get

or

Hence

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