Evaluate 19 sin(x) cos(x) dx by four methods. (a) the substitution u = cos(x) − 19 2 sin2(x) + C 19 4 cos(2x) + C 19 4 sin(x) cos(x) + C − 19 2 cos2(x) + C 19 4 sin(2x) + C (b) the substitution u = sin(x) 19 2 sin2(x) + C 19 4 cos(2x) + C 19 2 cos2(x) + C 19 4 sin(x) cos(x) + C − 19 4 sin(2x) + C (c) the identity sin(2x) = 2 sin(x) cos(x) − 19 2 sin2(x) + C − 19 4 sin(x) cos(x) + C − 19 4 cos(2x) + C 19 2 cos2(x) + C 19 4 sin(2x) + C (d) integration by parts − 19 4 sin(x) cos(x) + C 19 4 cos(2x) + C 19 2 sin2(x) + C − 19 4 sin(2x) + C 19 2 cos2(x) + C