Calculus II - Illinois State University

9.3.8 Using trig identities in integration Integrate. i) cos2 x sin3 x ii) cos2x cos3x iii) cos5x iv) cos 5x sin 3x v) sin 2x sin 3x. Solution. i) In a case like cos2 x sin3 x we remember that – sinx is the derivative of cos x and try to express everything in terms of cos x and it's derivative. With this in mind we have . cos2 x sin3 x dx = cos2 x sin2 x sin x dx = cos2 x (1 – cos2 x)sin x ... ................
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