Question

积分:sinx的五次幂.

Answer 1

因为sin^5x=sinx*sin^4x=sinx(1-cos^2x)^2

所以sin^5x=-dcosx(1-cos^2x)^2

令cosx=u,

原式=-du(1-u^2)^2

=-du(1+u^4-3u^2)

原式积分=-[u+(u^5)/5-u^3]

=-(1/5)cos^5x+cos^3x-cosx+C