Hvordan finder du integralet af int 1 / (1 + cos (x))?

Hvordan finder du integralet af int 1 / (1 + cos (x))?
Anonim

Svar:

# -Cotx + cscx + "C" #

Forklaring:

# int1 / (1 + cosx) dx = int (1-cosx) / ((1 + cosx) (1-cosx)) dx #

# = int (1-cosx) / (1-cos ^ 2x) dx #

# = int (1-cosx) / sin ^ 2xdx #

# = int 1 / sin ^ 2xdx-intcosx / sin ^ 2xdx #

=#int csc ^ 2xdx-intcotxcscxdx #

=# -Cotx + cscx + "C" #