(6)int_(0)^( pi)log(1+cos x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^( pi)log(1+cos x)dx

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi)log(1+cos x) dx

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) .

Find I=int_(0)^( pi)ln(1+cos x)dx

If int_(0)^(pi//2) ln (sin x) dx= - pi/2 ln 2 then int_(0)^(pi) ln (1+ cos x) dx=

int_(0)^((pi)/(2))log(cos x)dx=

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

If I(m)=int_(0)^( pi)ln(1-2m cos x+m^(2))dx then I(1)=