1)find g(x)=∫_0 ^(π/2) ln(1−x^2 cos^2 θ)dθ with x from R
2) find the value of ∫_0 ^(π/2) ln(1−2 cos^2 θ)dθ and
3) find the value of
A(α)=∫_0 ^(π/2) ln(1−cos^2 α cos^2 θ)dθ
let f(x)=∫_0 ^(π/2) ln(((1−xsint)/(1+xsint)))dt .
1) find the value of I = ∫_0 ^(π/2) ln(1−xsint)dt
and J = ∫_0 ^(π/2) ln(1+xsint)dt
2) find a simple form of f(x)
3) developp f at integr serie