Question

Qual a Integral ∫cos^6xdx?

Answer 1

∫cos⁶ˣdx                            u = 6x    du = 6dx   du/6 = dx

∫cos^u.du/6

1/6∫cos^u.du

1/6 sen^u  => 1/6 sen⁶ˣ + c

Answer 2

Resposta:

Explicação passo-a-passo:

$\int\limits \, cos^{6}xdx = \\\\= \frac{\sin \left(x\right)\cos ^5\left(x\right)}{6}+\frac{5}{6}\cdot \int \cos ^4\left(x\right)dx\\\\=\frac{\sin \left(x\right)\cos ^5\left(x\right)}{6}+\frac{5}{6}\left(\frac{1}{4}\cos ^3\left(x\right)\sin \left(x\right)+\frac{3}{8}\left(x+\frac{1}{2}\sin \left(2x\right)\right)\right) + c$