M-172Q Midterm: Montana State MATH 172 Exam 6
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Z cos3 x dx = z cos2 x cos x dx = z (1 sin2 x) cos x dx du=cos x dxz (1 u2) du u=sin x= = sin x sin3 x + c. u3 + c. Z sin5 2x cos2 2x dx = z (sin2 2x)2 cos2 2x sin 2x dx. = z (1 cos2 2x)2 cos2 2x sin 2x dx. 2 z (1 u2)2u2 du u=cos 2x= du= 2 sin 2x dx . 2 z (u2 2u4 + u6) du. 14 cos7 2x + c: if both are odd and positive, use either of the above, if both are even and positive, use the half-angle identities sin2 = 2 to rewrite until you have odd powers. Z sin4 3x dx = z (sin2 3x)2 dx = z (cid:18) 1 cos 6x. 4 z (1 2 cos 6x + cos2 6x) dx. 4 z (cid:18)1 2 cos 6x +
