Question

O valor da integral: cos³ x.sen^6 xdx é

Answer 1

$\displaystyle I=\int \cos^3 x\sin^6 x dx\\ \\ u=\sin x\to du =\cos xdx\\ \\ I=\int \cos^2 x\sin^6 x\;\cos xdx\\ \\ I=\int (1-u^2)u^6 du\\ \\ I=\int u^6-u^8 du\\ \\ I=\dfrac{u^7}{7}-\dfrac{u^9}{9}+C\\ \\ \\ \boxed{\boxed{I=\dfrac{\sin^7x}{7}-\dfrac{\sin^9x}{9}+C}}$