Question

calcule a integral:
∫ raiz cubica x^2 dx

Answer 1

Resposta:

∫ ∛x² dx

∫ x^(2/3) dx

= [x^(2/3+1)] / (2/3 +1)  + c

= [x^(2/3+1)] / (5/3)  + c

=(3/5)* x^(5/3) + c

=(3/5)* ∛x⁵ + c

Answer 2

Integral

Temos a Integral:

$\large \boxed{\boxed{\sf \displaystyle\int \sqrt[3]{x^{2} } \: dx}}$

Vamos Empurrar o índice 3, para baixo do 2, ficando com:

$\large \boxed{\boxed{\sf \displaystyle\int x^{\frac{2}{3} } \: dx}}$

Aplicando a Regra da Integração:

$\large \boxed{\boxed{\sf \displaystyle\int x^{n} \: dx=\frac{x^{n+1} }{n+1}+C }}$

• Cálculo:

$\large \boxed{\begin{array}{lr} \boxed{\begin{array}{lr} \sf \dfrac{x^{\dfrac{2}{3}+1 } }{\dfrac{2}{3} +1} \: +C \\\\\\ \sf \dfrac{x^{\dfrac{5}{3}} }{\dfrac{5}{3}} \: +C \end{array}} \: \end{array}}$

Resposta:

$\bullet \: \: \: \huge \boxed{\boxed{\sf \dfrac{\sf 3\sqrt[3]{x^{5} } }{5} + C }}$