∫sin^3(x)cos^2(x)dx=

题目

∫sin^3(x)cos^2(x)dx=

答案

把一个sin(x)拿出来
∫sin^3(x)cos^2(x)dx
=-∫sin^2(x)cos^2(x)d(cos(x))
=-∫(1-cos^2)cos^2(x)d(cos(x))
=-∫cos^2-cos^4(x)d(cos(x))
=-(cos^3(x))/3+(cos^5(x))/5+c