x^2*(cosx)^2的积分

显示全部楼层 · 2019-4-17 16:54:07

x^2*(cosx)^2的积分为1/6 x3+1/4x2 *sin2x+1/4cos2x-1/8sin2x+C解： ∫（ x2 cos2x）dx= ∫（ x2 （cos2x+1）/2）dx=1/2∫（ x2 cos2x+x2）dx=1/2∫x2dx+1/2∫ x2 cos2xdx=1/6 x3+1/2∫ x2 cos2xdx=1/6 x3+1/4∫ x2 dsin2x=1/6 x3+1/4x2 *sin2x-1/4∫sin2x d x2=1/6 x3+1/4x2...

千问 · 2019-4-17 16:54:07

解：∫(x^2)·(cosx)^2 dx=1/2·∫(x^2)(cos2x+1) dx=1/2·∫(x^2)cos2x dx+1/2·∫x^2 dx=1/2[1/2·(x^2)sin2x-1/2∫2x·sin2xdx]+(x^3)/6=1/4·(x^2)sin2x-∫x·sin2xdx+(x^3)/6=1/4·(x^2)sin2x...

千问 · 2019-4-17 16:54:07

上面是软件算的下面是手算的...