Hi there, yang03265...

Using parts we can first of all integrate log of x...

Straight lines integrate up or differentiate down, so that the triangular network satisfies the product rule for differentiation. The

challenge of integration by parts is simply to fill out this product shape usefully but starting (unlike when differentiating) with one of the lower

balloons.

We can use the above result to do your integral...

Now solve the top row for

Don't integrate - balloontegrate!

Balloon Calculus: worked examples from past papers