[tex] \int (sin(t)-cos(t)) \sqrt{cos^2(t)-sin^2(t)} dt [/tex](adsbygoogle = window.adsbygoogle || []).push({});

Is there a trig idendity I can use? I've distributed that root to both terms to get:

[tex] \int sin(t) \sqrt{cos^2(t)-sin^2(t)} dt -[/tex] [tex] \int cos(t) \sqrt{cos^2(t)-sin^2(t)} [/tex]

If I take one of the terms and integrate by parts, I'm trying to put [tex] u=\sqrt{cos^2(t)-sin^2(t)} [/tex] and [tex]dv= sin(t) [/tex] or [tex]dv= cos(t) [/tex] but that ugly root's derivative appears inside the [tex] \int vdu [/tex] part.

Is there a trig identity I'm missing, or some other tactic I could use? or could this just be reallyreallyugly math?

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# Homework Help: Confusing Trig/rational Integral

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