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

Find I=int_(0)^( pi)ln(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) .

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi)log(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)log(1+cosx)dx=-pi(log2)

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

If|a|lt 1, show that int _(0)^(pi)(log(1+a cos x ))/( cos x)dx =pi sin^(-1) a

If|a|lt 1, show that int _(0)^(pi)(log(1+a cos x ))/( cos x)dx =pi sin^(-1) a