Question

不定积分∫cosx(cos^2)3xdx

Answer 1

∫cosx(cos^2)3xdx=∫cosx*(1+cos6x)/2dx=1/2∫cosxdx+1/2∫cosxcos6xdx=1/2 *sinx+1/2∫cosxcos6xdx=1/2 *sinx+1/2∫[cos(x+6x)+cos(x-6x)]/2dx=1/2 *sinx+1/4∫[cos7x+cos5x]dx=1/2*sinx+1/20*sin5x+1/28*sin7x+C...