Question

Determinati primitiva functiei f (x)=x e^x ,pentru care F(1)=0

Answer 1

$\it F(x)=\int xe^x dx\\ \\ \int uv'=uv-\int u'v\\ \\ u=x \Rightarrow u'=1\\ \\ v'=e^x \Rightarrow v=e^x\\ \\ F(x)=xe^x-\int e^x dx=xe^x-e^x+\mathcal{C}=e^x(x-1)+\mathcal{C}\\ \\ F(1)=0 \Rightarrow e(1-1)+\mathcal{C}=0 \Rightarrow \mathcal{C}=0\\ \\ Primitiva\ cerut\breve{a}\ este\ F(x)=e^x(x-1)$