Question

Qual o passo a passo da integral de $\int\ {\frac{1}{sen^22x}} \, dx$?

Answer 1

$\displaystyle \sf \int\frac{1}{sen^2(2x)}dx \to \int cossec^2(2x)dx \\\\\\ Fa{\c c}amos : \\\\ u = 2x \to du = 2dx \to dx = \frac{1}{2}du \\\\\ Da{\'i}} : \\\\ \int cossec^2(u)\cdot \frac{1}{2}du \\\\\\ \frac{1}{2}\int cossec^2(u)du \\\\\\ \frac{1}{2}[-cotg(u)]+C \\\\\\ Portanto : \\\\ \int\frac{1}{sen^2(2x)}dx = \boxed{\sf \frac{-cotg(2x)}{2}+ C }\checkmark$