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

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

$$\int \frac{e^{x}x+e^x}{{xe}^x(1+{xe}^x)}dx$$$$let{xe}^x=z\Rightarrow ({xe}^x+e^x)dx=dz$$$$\int \frac{dz}{z(z+1)}$$$$=\int \frac{dz}{z}-\int \frac{dz}{z+1}$$$$=ln\mid z\mid -ln\mid z+1\mid +c[z={xe}^x]$$

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

$$\mathrm{thanks}$$

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