Question

Integral Indefinida de: ∫$\sqrt[3]{8(t-2)^{6} (t+ \frac{1}{2})^{3} }$

Answer 1

$\int \sqrt[3]{8*(t-2)^6*(t+ \frac{1}{2})^3 }\;dt \\\\=\int\left[ \sqrt[3]{8}* \sqrt[3]{(t-2)^6}*\sqrt[3]{(t+ \frac{1}{2})^3} \right]dt\\\\=\int \left[2*(t-2)^2*(t+ \frac{1}{2}) \right]\\\\ =\int\left[2*(t-2)^2*( \frac{2t+1}{2}) \right]dt\\\\=\int (t-2)^2*(2t+1)dt\\\\=\int(t^2-4t+4)*(2t+1)dt\\\\\boxed{\boxed{= \int (2t^3-7t^2+4t+4)dt= \frac{t^4}{2} -\frac{7t^3}{3}+2t^2+4t+C }}$