微积分求解：∫sin^3 (x) cos^2 (x) dx

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/10 18:05:21

微积分求解：∫sin^3 (x) cos^2 (x) dx
如题.

∫sin^3 (x) cos^2 (x) dx
=∫sin^2 (x) cos^2 (x)sin(x)dx
=-∫sin^2 (x) cos^2 (x)dcos(x)
=∫[cos^2 (x)-1]cos^2 (x)dcos(x)
设cos(x)=u
上式=∫(u^2-1)u^2du
=∫(u^4-u^2)du
=(u^5)/5-(u^3)/3+C
=cos^5(x)/5-cos^3(x)/3+C

微积分求解：∫sin^3 (x) cos^2 (x) dx 求微积分 ∫sin^2(x)cos^4(x) dx cos^3(2x)sin(2x)dx求解微积分求解：∫(e^x) cos(x) dx 微积分求解∫e^x cos(e^x)dx= 求解 ∫sin(6x)^3*cos(6x)^8 dx=? 范围[pi/2,0] 微积分：∫sin²(2x+1)cos(2x+1)dx谢谢. 微积分求不定积分 ∫ [(cos2x) / (cos^2x * sin^2x)] dx ∫sin(x) cos^2(x)dx 微积分求解：∫x / (x+1) dx 求积分：∫sin^2 (x) /cos^3 (x) dx ∫ [cos^3(x)]/[sin^2 (x)]dx