let f(x) =∫ (dt/(x +cost +cos(2t))) (x real)
1) find a explicit form of f(x)
2)determine also ∫ (dt/((x+cost +cos(2t))^2 ))
3) find ∫ (dt/(1+cos(t)+cos(2t))) and
∫ (dt/((3 +cos(t)+cos(2t))^2 ))
let f(x) =∫_(π/4) ^(π/3) (dt/(2+xsint))
1) find a explicit form of f(x)
2)determine also g(x)=∫_(π/4) ^(π/3) ((sint)/((2+xsint)^2 ))dt
3) find the value of ∫_(π/4) ^(π/3) (dt/(2+3sint))
and ∫_(π/4) ^(π/3) ((sint)/((2+3sint)^2 ))dt