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Prologue

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## Homework Statement

[tex]\int \frac{x}{x+d}dx[/tex]

## The Attempt at a Solution

I tried parts and that turned out horribly so I fired up maple. First move it makes is 'Rewrite Rule'. I've never heard of a rewrite rule but I supposed it could be some algebraic massaging. I ended up looking at it this way:

[tex]\frac{x}{x+d} = 1-1+\frac{x}{x+d} = \frac{x+d}{x+d}-\frac{x+d}{x+d}+\frac{x}{x+d} = \frac{x+d}{x+d}+\frac{x-d-x}{x+d} = 1-\frac{d}{x+d}[/tex]

Which then is easily integrable. My question is, is there a snappier way to think of this/do it?