Question-166940

Question Number 166940 by cortano1 last updated on 03/Mar/22

Answered by som(math1967) last updated on 03/Mar/22

\int \frac{e^{x} x + e^{x}}{{x e}^{x} (1 + {x e}^{x})} d x

l e t {x e}^{x} = z \Rightarrow ({x e}^{x} + e^{x}) d x = d z

\int \frac{d z}{z (z + 1)}

= \int \frac{d z}{z} - \int \frac{d z}{z + 1}

= l n ∣ z ∣ - l n ∣ z + 1 ∣ + c [z = {x e}^{x}]

Commented by peter frank last updated on 03/Mar/22

thanks