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Question Number 87769 by john santu last updated on 06/Apr/20

$$\int \frac{\ln ({\mathrm{e}}^{\mathrm{x}}+1)}{{\mathrm{e}}^{-\mathrm{x}}+1}\mathrm{dx}$$

Answered by TANMAY PANACEA. last updated on 06/Apr/20

$$\int \frac{e^{x}ln(e^x+1)}{e^x+1}dx$$$$t=ln(e^x+1)\to \frac{dt}{dx}=\frac{e^x}{e^x+1}$$$$\int tdt=\frac{t^2}{2}+c$$$$\frac{{\left\{ln(e^x+1)\right\}}^2}{2}+c$$

Answered by john santu last updated on 06/Apr/20

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