Integration by Parts: Example 1

Evaluate

Let us follow the steps

1

This is an indefinite integral involving one function. The second needed function is g(x) = 1. Since the derivative of this function is 0, the only choice left is to differentiate the other function .

2

We have

which gives

3

We have the formula

4

Since

we get

Since the derivative of is 1/x, it is very common that whenever an integral involves a function which is a product of with another function, to differentiate and integrate the other function.

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