Question

Интеграл (x-1)e^x*xdx

Answer 1

$Largeint(x-1)e^x*xmathrm{dx}=int(x^2cdot e^x-xcdot e^x)mathrm{dx}=int e^xcdot x^2mathrm{dx}-int e^xcdot xmathrm{dx}=left [ u=x^2,du=2x: dx;: dv=e^x: dx, v=e^x right ]=e^xcdot x^2-2int e^xcdot xmathrm{dx}-int e^xcdot xmathrm{dx}=e^xcdot x^2-3int e^xcdot xmathrm{dx}=left [ u=x, du=dx;dv=e^x: dx,v=e^x right ]=e^xcdot x^2-3(e^xcdot x-int e^xmathrm{dx})=e^xcdot x^2-3e^xcdot x+3e^x+C=e^xcdot(x^2-3x+3)+C$