Como calcular a integral de (x + arcsen1)^-1.... Pergunta de ideia deMhary11

Mhary11 @Mhary11

December 2019 1 85 Report

Como calcular a integral de (x + arcsen1)^-1

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niltonjr2001 $\textbf{Resolveremos por substitui\c{c}\~ao u.du:}\\\\ \mathrm{u=x+\arcsin{1}\ \ \|\ \ \dfrac{du}{dx}=1\ \to\ du=dx}\\\\ \mathrm{\int(x+\arcsin{1})^{-1}\ dx=\int u^{-1}\ du=\int\dfrac{1}{u}\ du=\ln{|u|}+C}\\\\ \mathrm{*\ Como\ u=x+\arcsin{1}\ \to\ \ln{|x+\arcsin{1}|}+C}\\\\ \boxed{\mathbf{\int(x+\arcsin{1})^{-1}\ dx=\ln{\bigg|1+\dfrac{\pi}{2}\bigg|}+C}}$

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