The first is by parts (integrating 1 and differentiating the integral), re-writing

as

Will post a pic. The others look similar.

Edit: Just in case a picture helps...

... where...

is the product rule for differentiation (top to bottom).

In balloon world, integration by parts is a matter of filling out the product rule shape usefully, but starting in one of the bottom corners rather than (as with differentiation) the top one... and then subtracting whatever it's necessary to subtract on the bottom row, in order to keep the lower equals sign valid.

One blank to fill in the top row, then solve the top row for I.

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Don't integrate - balloontegrate!

http://www.ballooncalculus.org/forum/top.php