x的三次方*cosx的不定积分用分部积分法怎么做?这种类型的题最简单的方法就是分步积分?

Question

x的三次方*cosx的不定积分用分部积分法怎么做?这种类型的题最简单的方法就是分步积分?

Answer 1

=sin(x)*x^3-∫sin(x)*3x^2dx
=sin(x)*x^3-3[-cos(x)*3x^2-∫-cos(x)*6xdx]
=sin(x)*x^3+3cos(x)*3x^2-3∫cos(x)*6xdx
=sin(x)*x^3+3cos(x)*3x^2-18[sin(x)*x-∫sin(x)dx]
=sin(x)*x^3+3cos(x)*3x^2-18sin(x)*x-cosx
求积分的话可能还要加上一个常数项C