Resolva a Integral. Integral (x^3 +2/raiz de X)^2 dx Obs: A raiz de X fica de baixo so do 2.... Pergunta de ideia deHggjgg

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Resolva a Integral.

Integral (x^3 +2/raiz de X)^2 dx

Obs: A raiz de X fica de baixo so do 2.

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$\displaystyle \int (x^3+\frac{2}{ \sqrt{x} } )^2dx \\ \\ \\ \int(x^3+2x^-^ \frac{1}{2} )^2dx \\ \\ \\ \text{basta desenvolver esse quadrado} \\ \\ \\ \int(x^6+4x^ \frac{5}{2} + \frac{4}{x} )dx \\ \\ \\ \int x^6dx~+~4\int x^ \frac{5}{2}dx+4\int \frac{dx}{x} 
 \\ \\ \\ = \frac{x^7}{7} ~+~4( \frac{x^ \frac{7}{2} }{ \frac{7}{2} } )~+~4\cdot ln|x| \\ \\ \\ = \frac{x^7}{7} ~+~4( \frac{2x^ \frac{7}{2} }{7} )~+~4\cdot ln|x| \\ \\ \\$

$\boxed{\boxed{= \frac{x^7}{7} + \frac{8x^\frac{7}{2} }{7} +4\cdot ln|x|+C}}$

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