Question

Dado a integra sen³(x).cos(x)dx¹ qua seria a resposta?

Answer 1

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