" NCERT EXEMPLARJ "quad " (ii) "log{(a+b sin x)/(a-b sin x)}

int_0^(pi/2) log ((a+b sin x)/(a+b cos x)) dx =

Differentiate w.r.t. 'x' : f(x) = log((a+b sin x)/(a - b sin x))

Differentiate w.r.t. 'x' : f(x) = log((a+b sin x)/(a - b sin x))

(sin x)^(log x)

int (cos x)/( sin x log sin x)dx=

Differentiate log{(a+b sin x)/(a-b sin x)} with respect to x:

y = A cos (log x) + B sin (log x)

If y=(sin x)^(tan x), then (dy)/(dx)= (a) (sin x)^(tan x)(1+sec^(2)x log sin x)(b)tan x(sin x)^(tan x-1)cos x(c)(sin x)^(tan x)(d)sec^(2)x log sin x tan x(sin x)^(tan x-1)

Can anyone prove int_(-(pi)/(2))^((pi)/(2))((log(1+b sin x))/(sin x))dx=pi sin^(-1)b, where |b|<1

If int (1)/(sin (x -a ) cos (x -b)) dx = A log | (sin (x -a))/( cos (x -b ))| + B. Then