Respuesta:
Explicación:
[tex]\int \frac{sin(x)}{cos^{2}(x) } dx[/tex]
sea t = cos (x)
dt = - sin (x) dx => - dt = sin (x) . dx
sustituye
[tex]\int \frac{-dt}{t^{2} } = -\int \frac{dt}{t^{2} }[/tex]
[tex]\int \frac{-dt}{t^{2} } = -\int t^{-2} dt = - \int \frac{t^{-2+1} }{-2+1} dt= - \int \frac{t^{-1} }{-1} dt = \int\frac{1}{t}dt= Ln (t) + C[/tex]
Retorna de nuevo a la variable x
[tex]\int \frac{sin(x)}{cos^{2}(x) } = Ln [cos(x)]+ C[/tex]
