Question

calcule a integral indefinida por partes (x-1)e^xdx

Answer 1

Resposta:

∫  (x-1) * e^(x) dx = ∫  x* e^(x) dx - ∫ e^(x) dx

∫ e^(x) dx=e^(x) +c₁

∫  x* e^(x) dx

******u=x ==>du=dx

******e^(x) dx =dv ==> ∫ e^(x) dx =∫dv ==>e^(x) =v

∫  x* e^x dx  =x*e^(x) - ∫  e^(x) dx = x*e^(x) -e^(x)  + c₂

∫  (x-1) * e^(x) dx =-e^(x)  +c₁ + x*e^(x) -e^(x)  + c₂

*******Fazendo c₁ + c₂ =c , ficamos com

∫  (x-1) * e^(x) dx = -e^(x)  + x*e^(x) -e^(x)  + c

=-2e^(x) +x*e^(x) +c

=e^(x) * (x-2) + c