Question

A integral indefinida de ∫▒〖x^2√ᵪ³〗-1 dx é

Answer 1

$\mathrm{\int x^2\sqrt{x^3}\ dx=\int x^2.x^{\frac{3}{2}}\ dx=\int x^{2+\frac{3}{2}}\ dx=}\\\\ \mathrm{=\int x^{\frac{4}{2}+\frac{3}{2}}\ dx=\int x^{\frac{7}{2}}\ dx=\dfrac{x^{\frac{7}{2}+1}}{\frac{7}{2}+1}=\dfrac{x^{\frac{7}{2}+\frac{2}{2}}}{\frac{7}{2}+\frac{2}{2}}=\dfrac{x^{\frac{9}{2}}}{\frac{9}{2}}=\dfrac{2x^{\frac{9}{2}}}{9}}\\\\ \mathrm{\int x^2\sqrt{x^3}\ dx=\boxed{\mathbf{\dfrac{2x^{\frac{9}{2}}}{9}+C}}\ \ ou\ \ \boxed{\mathbf{\dfrac{2x^4\sqrt{x}}{9}+C}}}$