9x=int lg(+ax)+a+xydu=pi log2

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

If int_(0)^(pi//2) log(cosx) dx=pi/2 log (1/2), then int_(0) ^(pi//2) log (sec x ) dx =

Prove that int_(-pi//4)^(pi//4) log(sinx + cosx)\ dx = -pi/4\ log2.

Show that int_(0)^(pi//2) log (sin x) dx = - pi/2 log 2

Prove that int log sin x dx = - (pi/2)log2

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

Prove that: int_(0)^(pi//2) log (sin x) dx =int_(0)^(pi//2) log (cos x) dx =(-pi)/(2) log 2

Prove that: int_(0)^( pi/2)log|tan x+cot x|dx=pi log_(e)2

Prove that int_(0)^(pi//2)log (sinx)dx=int_(0)^(pi//2) log (cosx)dx=-(pi)/(2) log 2 .