Question

Integral definida de
( 1+1/x) dx de 1 ate euler


Resposta : e

Answer 1

Olá Lara!

$\\ \displaystyle \mathsf{\int_{1}^{e} \left ( 1 + \frac{1}{x} \right ) \ dx} \\\\\\ \mathsf{\int_{1}^{e} 1 \ dx + \int_{1}^{e} \frac{1}{x} \ dx =} \\\\\\ \mathsf{\left [ x \right ]_{1}^{e} + \left [ \ln x \right ]_{1}^{e} =} \\\\\\ \mathsf{\left ( e - 1 \right ) + \left ( \ln e - \ln 1 \right ) =} \\\\ \mathsf{e - 1 + 1 - 0 =} \\\\ \boxed{\mathsf{e}}$


 Obs.: $\mathsf{\ln e = \log_e e = 1}$.

Answer 2

$\displaystyle\mathsf{\int\limits_{1}^{e}(1+\dfrac{1}{x})dx=(x+ln|x|)\Bigg|_{1}^{e}}\\=\mathsf{e+ln(e)-(1+ln(1))=e+1-1-0}\\=\large\boxed{\boxed{\boxed{\boxed{\mathsf{e}}}}}$