Let `f(a)=int_0^a ln(1+tanatanx)dx`, then `f'(pi/4)` equals:

int_0^(pi//2)log(tanx)dx

Let a in(0,(pi)/(2)) ,then the value of lim_(a rarr0)(1)/(a^(3))int_(0)^(a)ln(1+tan a tan x)dx is equal to

Let F (x) = f(x) + f ((1)/(x)), where f (x) = int _(1) ^(x ) (log t)/(1+t) dt. Then F (e) equals

int_({1+tan x*tan(x+A)}dx)=cot A*ln|f(x)|+C then f(x) equal to

int_(0)^(pi//4) log (1+tan x) dx =?

Let I_(1) =int_(a)^(pi-a)xf(sinx)dx,I_(2)=int_(a)^(pi-a)f(sinx)dx , then I_(2) is equal to