Question

o valor da integral indefinida

Answer 1

Integração por substituição. Resposta na imagem.

Answer 2

$\textrm{Resolveremos a integral pelo m\'etodo}\\ \textrm{de substitui\c{c}\~ao u.du}:\\\\ \mathrm{u=e^{2x}+2\ \ \| \ \ \dfrac{du}{dx}=2.e^{2x}\ \to\ \dfrac{du}{2}=e^{2x}.dx}\\\\ \mathrm{\int(e^{2x}+2)^5.e^{2x}\ dx=\int u^5.\dfrac{1}{2}\ du=\dfrac{1}{2}\int u^5\ du=}\\\\ \mathrm{=\dfrac{1}{2}.\dfrac{u^6}{6}=\dfrac{u^6}{12}=\mathbf{\dfrac{(e^{2x}+2)^6}{12}+c}}$