No need for integration by parts, use trigonometric identities.
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http://www.ballooncalculus.org/forum...lllpartslllone
Ok, it's a video, but my link is to a .wmv file and I need to do it differently, clearly. Will fix. (Edit: fixed, but you have to follow the link to see the video - was hoping it would project right here!)
Anyway, just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!