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Question-188544




Question Number 188544 by 073 last updated on 03/Mar/23
Answered by ARUNG_Brandon_MBU last updated on 03/Mar/23
∫(e^(arctanx) /(1+x^2 ))dx+(1/2)∫((2xln(1+x^2 ))/(1+x^2 ))dx+∫(1/(1+x^2 ))dx  =e^(arctanx) +((ln^2 (1+x^2 ))/4)+arctanx+C
$$\int\frac{{e}^{\mathrm{arctan}{x}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}+\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{2}{x}\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}+\int\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$={e}^{\mathrm{arctan}{x}} +\frac{\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{4}}+\mathrm{arctan}{x}+{C} \\ $$
Commented by CElcedricjunior last updated on 05/Mar/23
good!
$${good}! \\ $$

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