# Mike Lawler Inspired Integration

Back in March I saw the tweet shown below from Mike Lawler (@mikeandallie).

I think I would default to substituting $$u = \mathrm{e}^x$$ here but in the thread were a range of different approaches. Tim Gower’s (@wtgowers) was particularly inventive.

I’ve always enjoyed asking students to integrate things in different ways and then asking them to show their solutions are equivalent. A favourite one of mine is $$\int \sin(x) \cos(x) \ \mathrm{d}x$$. Because of this I have made a sheet asking students to explore a few of the possible methods.