(1)/(4+5sin x)

Evaluate : int (1)/(4+5 sin x)dx

Evaluate : int (1)/(4+5 sin x)dx

int(1)/(5-4 sin x)dx

int(1)/(5-4 sin x)dx

Evaluate int(1)/(5+4sin x)dx

Evaluate: int(1)/(5-4sin x)dx

Evaluate: int(1)/(5-4sin x)dx

A: int (1)/(5+4 sin x)dx=(2)/(3) Tan^(-1)((4+5tan (x//2))/(3))+c R : If a gt 0, a gt b , then int (dx)/(a+b sin x)=(2)/(sqrt(a^(2)-b^(2)))Tan^(-1)[(b+a tan (x//2))/(sqrt(a^(2)-b^(2)))]+c

int(1)/(5+4sin x)dx=A tan^(-1)(B(tan x)/(2)+(4)/(3))+C, then A=(2)/(3),quad B=(5)/(3)(b)A=(1)/(3),quad B=(2)/(3)(c)A=-(2)/(3),B=(5)/(3)(d)A=(1)/(3),quad B=-(5)/(3)

(1) int(dx)/(5+4 sin x)