Come trovi l'integrale di $\int \frac{1}{1 + cos (x)}$ $int 1 / (1 + cos (x))$ ?

$- cot x + csc x + C$ $-cotx+cscx+"C"$

$\int \frac{1}{1 + cos x} d x = \int \frac{1 - cos x}{(1 + cos x) (1 - cos x)} d x$ $int1/(1+cosx)dx = int(1-cosx)/((1+cosx)(1-cosx))dx$

$= \int \frac{1 - cos x}{1 - {cos}^{2} x} d x$ $= int(1-cosx)/(1-cos^2x)dx$

$= \int \frac{1 - cos x}{{sin}^{2} x} d x$ $= int(1-cosx)/sin^2xdx$

$= \int \frac{1}{{sin}^{2} x} d x - \int \frac{cos x}{{sin}^{2} x} d x$ $= int 1/sin^2xdx-intcosx/sin^2xdx$

= $\int {csc}^{2} x d x - \int cot x csc x d x$ $int csc^2xdx-intcotxcscxdx$

= $- cot x + csc x + C$ $-cotx+cscx+"C"$

Come trovi l'integrale di ∫11+cos(x)int 1 / (1 + cos (x)) ?