Question

Um exercício de Integral em anexo abaixo:

Answer 1

$\int \frac{5}{3}* \sqrt[3]{x^2} dx\\\\ \frac{5}{3}*\int x^{ \frac{2}{3} }dx\\\\= \frac{5}{3}*( \frac{x^{ \frac{2}{3}+1 }}{ \frac{2}{3}+1 } ) \\\\= \frac{5}{3}*( \frac{x^{ \frac{5}{3} }}{ \frac{5}{3} } ) \\\\= \frac{5}{3}*( \frac{3x ^\frac{5}{3} }{5} ) \\\\= x^ \frac{5}{3}+C \\\\= \sqrt[3]{x^5}+C$

Answer 2

$\int \frac{5}{3} . \sqrt[3]{ {x}^{2} } dx \\ \int \frac{5}{3} . {x}^{ \frac{2}{3} } dx \\ \\ \frac{5}{3} \int \frac{ {x}^{ \frac{2}{3} + 1 } }{ \frac{2}{3} + 1} \\ \\ \frac{5}{3} \int \frac{ {x}^{ \frac{5}{3} } }{ \frac{5}{3} } \\ \\ \frac{5}{3} \int \frac{3}{5} . {x}^{ \frac{5}{3} } \\ \\ \frac{5}{3} . \frac{5}{3} . {x}^{ \frac{3}{5} } = \frac{15}{15} . {x}^{ \frac{5}{3} }=</p><p></p><p> \\ {x}^{ \frac{5}{3} }= \\ \\ \sqrt[3]{ {x}^{5} } + c$