Question

Calcule a integral indefinida.
(Por favor não responda só pra ganhar ponto, estou desesperadaa!)

Answer 1

$\displaystyle \int\text{sen(t)sec}^2(\text{cos(t)})\text{dt} \\\\\\ \underline{\text{Fa{\c c}amos}}: \\\\ \text{cos(t)}=\text u \to -\text{sen(\text t)\text{dt}}=\text{du} \\\\ \text{Da{\'i}}: \\\\ \int -\text{sec} ^2(\text{u})\text{du} \\\\\\ -\int \text{sec}^2(\text u)\text{du}=-\text{tan} (\text{u}) +\text C\to -\text{tan(cos(t))}+\text C \\\\\\ \int \text{sen(t)sec}^2(\text {cos(t))dt}=\huge\boxed{-\text {tan(cos(t))+C}}\checkmark$