Integral from Cambridge STEP Paper.

Show, by means of a suitable change of variable, or otherwise, that

Hence, or otherwise, show that

This is taken directly from STEP 1, 1998. Now the challenge isn't finding a solution, that's cake for many of you, the challenge is explaining it to me. A maths student in the first year of sixth-form (I think you call it high-school in America.) I've never seen integrals like these before, the most advanced form of integration I've used is integrations by parts.

Please explain EVERYTHING!