The acceleration of an object moving in a strange way has
been modelled as:
a = x ∙ e^x
Use integration by parts to find an equation to model the
velocity, v, given that v = ∫ x ∙ e^x dx
let p=xp=xp=x and dr=exdxdr=e^{x}dxdr=exdx
=>dp=dx=>dp=dx=>dp=dx and r=exr=e^{x}r=ex
∫pdr=pr−∫rdp\smallint{pdr}=pr-\smallint{rdp}∫pdr=pr−∫rdp
v=∫xexdx=xex−∫exdxv=\smallint{xe^{x}dx}=xe^{x}-\smallint{e^{x}dx}v=∫xexdx=xex−∫exdx
=>v=xex−ex+c=ex(x−1)+c=>v=xe^{x}-e^{x}+c=e^{x}(x-1)+c=>v=xex−ex+c=ex(x−1)+c
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