Question

Calculo dessa integral $\int\limits^1_0 {} \,$ e^(-x)*(4-e^x) dx

Answer 1

$\int\limits^1_0 {(e^{-x}(4-e^x))} \, dx \\ \\ \int\limits^1_0 {(4e^{-x}-1)} \, dx \\ \\ 4\int\limits^1_0 {e^{-x}} \, dx-\int\limits^1_0 {} \, dx \\ \\ -4e^{-x} \ |^1_0 - x \ |^1_0 \\ \\ -4(e^{-1}-e^{-0})-(1-0) \\ \\ -\frac{4}{e} +4-1 \\ \\ \boxed{ -\frac{4}{e} +3}$