Question

Alguem ajuda nessa resoluçao com explicaçao por favor

Answer 1

Integrais de potências:

$\boxed{\boxed{\displaystyle\int x^{n}dx=\dfrac{x^{n+1}}{n+1}+C~~para~todo~n\neq-1}}$

C: Constante de integração
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$\displaystyle\int(x^{3}\sqrt{x})dx=\int(x^{3}\cdot x^{1/2})dx\\\\\\\int(x^{3}\sqrt{x})dx=\int(x^{3+(1/2)})dx\\\\\\\int(x^{3}\sqrt{x})dx=\int(x^{7/2})dx\\\\\\\int(x^{3}\sqrt{x})dx=\dfrac{x^{(7/2)+1}}{(\frac{7}{2})+1}+C\\\\\\\int(x^{3}\sqrt{x})dx=\dfrac{x^{9/2}}{(\frac{9}{2})}+C\\\\\\\boxed{\boxed{\int(x^{3}\sqrt{x})dx=\dfrac{2}{9}x^{\frac{9}{2}}+C}}$