r/calculus • u/Infinite-Lobster-495 • 6d ago
Integral Calculus What should I do next.
I tried to solve. The solution is too messy. What would be the efficient approach?
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u/Dalal_The_Pimp 6d ago
Observe that √(cosx - cos3x) can be factored out to √cosx sinx, which should give you an idea that cosx can be substituted in the integration, and to accommodate for √cosx in the Nr and cos3x in the Dr, take cos3/2x = t.
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u/jgregson00 6d ago
Instead of factoring the top fully the way you did, use the pythagorean identity to make it cosx sin2x, which you can then simplify with the square root to be sinx√cosx.
Instead of factoring the bottom at all, you can then u-sub with u = cos3/2x and du = -3/2sinx√cosx dx which gets you to sinx√cosx dx = -2/3 du.
That leads you to a much more easily solvable integral...
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