[" 45.(a) "log(ax+b)/(cx+d)," (b) "sqrt(cosec x cot x)," (c) "cos^(3)(3x^(3))]

log("cosec x"-cot x)

(d)/(dx) {log (sqrt(cosec x +1)- sqrt(cosec -1))}=

itn "cosec" x log ("cosec" x-cot x)dx=

(d)/(dx)(log tan((pi)/(4)+(x)/(2)))= (a) cosec x (b) -cosec x (c) sec x (d) -sec x

int e^(-x) cosec x(1+ cot x) dx is equal to a) e^(-x) cosec x + C b) -e^(-x) cosec x + C c) - e^(-x) ( cosec x + cot x ) + C d) - e^(-x) ( cosec x - tan x ) + C

y= 4 ^(log _ 2 cosec x)- 9 ^(log_3 cot x) ,then (dy)/(dx) =

Integrate the following with respect to x. (i) sin(2x +4) " " (ii) "sec"^2 (3 + 4x) " " (iii) "cosec" (ax + b) cot (ax + b) .

int_( then )^( If )(dx)/(cos(x)/(3)sin^(3)(x)/(3))=A ln cot(x)/(3)+B cot^(2)(x)/(3)+c

int frac {x+1}{x+2} dx =............ A) x+2 - log(x+2) + c B) sqrt (x^2 + 3x +2) -(1/2) log x + (3/2) + sqrt (x^2 + 3x +2) + c C) sqrt (x^2 + 3x +2) +(1/2) log x + (3/2) + sqrt (x^2 + 3x +2) + c D) sqrt (x^2 + 3x +2) -(1/2) log x + (3/2) - sqrt (x^2 + 3x +2) + c