∫xsinxdx用分部积分和凑积分两种表达?

Question

∫xsinxdx 用分部积分和凑积分两种表达?

Answer 1

u=x,v=-cos(x),
\int u v' dx = uv - \int u' v dx
where \int means integral.
What do you mean by "凑积分"?
Probably,
\int x sin(x) dx = -\int x d(cos(x))
y=cos(x)
Then,
\int x d(cos(x)) = \int arccos(y) dy
Then subsitute y by cos(x).
Good luck~!