Question

Encontre a integral indefinida dada | ( cós( x))³. Sim(x)dx

Answer 1

$\displaystyle \sf \int [cos(x)]^3\cdot sen(x)dx \\\\\\ -1\cdot \int [cos(x)]^3\cdot [-sen(x)]dx \\\\\\ \text{Fa{\c c}amos } : \\\\ cos(x) = u \to -sen(x)dx = du \\\\ Da{\'i}}: \\\\ -\int u^3du = -\frac{u^4}{4}+C =-\frac{cos^4(x)}{4}+C \\\\ Portanto :\\\\ \boxed{\sf \ \int [cos(x)]^3\cdot sen(x)dx = \frac{-cos^4(x)}{4}+C\ }\checkmark$