let `f(a)=int_(0)^(a)ln(1+tan a tan x)dx` then `f'((pi)/(4))` equals

Let f(a) = int_0^a(ln(1+tana. tanx)dx then f'(pi/4)

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

The value of int_(0)^(a) log ( cot a + tan x) d x , where a in (0,pi//2) is equal to

If f(x)=int_(1)^(x) (log t)/(1+t) dt"then" f(x)+f((1)/(x)) is equal to

Evaluate int_(0)^(pi//4) log (1+tan theta)d theta

For f(x) =x^(4) +|x|, let I_(1)= int _(0)^(pi)f(cos x) dx and I_(2)= int_(0)^(pi//2) f(sin x ) dx "then" (I_(1))/(I_(2)) has the value equal to

Evaluate : int_(0)^(pi//4) tan ^(2) x dx

The value of the integral I=int_(0)^(pi)(x)/(1+tan^(6)x)dx, (x not equal to (pi)/(2) ) is equal to

If f(x)=-int_(0)^(x) log (cos t) dt, then the value of f(x)-2f((pi)/(4)+(x)/(2))+2f((pi)/(4)-(x)/(2)) is equal to

int_(0)^( pi/4)tan^(3)dx