Question

integral da raiz quadrada 7x+3dx

Answer 1

Boa tarde!

Solução!

$\displaystyle\int \sqrt{7x+3}dx$

$u= \sqrt{7x+3} ~~~~~x= \dfrac{u^{2}-3 }{7} \\\\\\\ dx= \dfrac{2u}{7} du$

$\displaystyle\int u. \frac{2u}{7}\\\\\\\ \frac{2}{7} \displaystyle\int u.u\\\\\\\ \frac{2}{7} \displaystyle\int u^{2} \\\\\\\ I=\frac{2}{7}. \frac{u^{3} }{3} \\\\\\\\ I= \frac{2u^{3} }{21}\\\\\\\\ I=\frac{2(\sqrt{7x+3}) ^{3} }{21}+C$


$\boxed{Resposta:~~\displaystyle\int \sqrt{7x+3}dx =\frac{2( \sqrt{7x+3}) ^{3} }{21}+C}}$




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Bons estudos!