Question

qua é a integral indefinida de x/x+1 dx

Answer 1

Calcular a integral indefinida:

     $\mathsf{\displaystyle\int\frac{x}{x+1}\,dx}\\\\\\ =\mathsf{\displaystyle\int\frac{x+1-1}{x+1}\,dx}\\\\\\ =\mathsf{\displaystyle\int\left(\frac{x+1}{x+1}-\frac{1}{x+1}\right)\,dx}\\\\\\ =\mathsf{\displaystyle\int\left(1-\frac{1}{x+1}\right)\,dx}\\\\\\ =\mathsf{\displaystyle\int 1\,dx-\int\frac{1}{x+1}\,dx}$

     $=\mathsf{x-\ell n|x+1|+C\quad\longleftarrow\quad esta~\acute{e}~a~resposta.}$


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