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int(A+B=)^(1f)(1)/(5+4sin x)dx=A tan^(-1...

int_(A+B=)^(1f)(1)/(5+4sin x)dx=A tan^(-1)(B(5td)

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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)

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

If int ( dx )/(5 + 4 sin x) = A tan^(-1) ( B tan ((x)/(2)) + (4)/(3)) + C , then :

If int ( dx )/(5 + 4 sin x) = A tan^(-1) ( B tan ((x)/(2)) + (4)/(3)) + C , then :