Question

积分号sin^(4)x,这个不定积分怎么积分啊?

Answer 1

∫(sinx)^4 dx=∫[(sinx)^2]^2 dx=∫[(1-cos2x)/2]^2 dx=1/4·∫[1-2cos2x+(cos2x)^2] dx=1/4·∫[1-2cos2x+(1+cos4x)/2] dx=1/4·∫[3/2-2cos2x+(cos4x)/2] dx=1/4·[∫3/2 dx-∫2cos2x dx+1/2·∫ (cos4x) dx]=1...