Simplify each expression.

8.1 Integration by Parts ❑ ❑ ❑ ❑ ❑ Deals with: ∫ xe dx, ∫ xcos(2 x)dx∫, l| | d∫ , e c(x)dx , etc… ❑ ❑ ❑ ❑ Consider: u(x) & v(x) 2❑different❑able functions: (❑*v)’=(u*v’)+(u❑*v) &(integrate ' with respect to x) uv= ∫ uv )dx+∫(u' v)dx ∫ uv' dx=uv- ∫ u' vdx ❑ ❑ ❑ ❑ ❑ ❑ udv=uv− vdu ❑ ∫❑ x x xe dx u=x dv=e dx du=dx v=e x Ex. ❑ *Let dv be the easiest part of the integrand ¿ ∫❑ ❑ ❑ ❑ x x x x❑ x x ∫ xe dx=xe − e∫dx ∫ xe dx=xe −e +C ❑ ❑