Cos ^nxsin^nx=1/2^ncos^nx第十五题

\u79ef\u5206x^2*cos(nx)

\u5bf9\uff0c\u7528\u5206\u90e8\u79ef\u5206\u505a

\u3002\u3002\u3002\u3002\u3002

\u7ed3\u679c\u662f
(2xcosnx)/n^2+
[(n^2*x^2-2)sinnx]/n^3

(3x^2+1)cos(nx)\u539f\u51fd\u6570 = (3x^2 cos(nx) + cos(nx))\u539f\u51fd\u6570

\u79ef\u5206 cos(nx)dx = sin(nx)/n

\u79ef\u5206 x^2 cos(nx) dx = \u79ef\u5206 x^2 d(sin(nx)/n) = x^2sin(nx)/n - (1/n)\u79ef\u5206 sin(nx) d(x^2)

\u79ef\u5206 sin(nx) d(x^2) = 2\u79ef\u5206 xsin(nx) dx

\u79ef\u5206 xsin(nx) dx = \u79ef\u5206 x d(-cos(nx)/n) = xcos(nx)/n + (1/n)\u79ef\u5206cos(nx) dx

\u79ef\u5206 cos(nx)dx = sin(nx)/n

扩展阅读：lim x-sinx ... xdx ... f x sin2xsin3x ... cos nx ds dydz ... sec x ... sin nx ... sin4x ... cosplay图 ... ∫x cos3xdx ...