If $\int\left(1+x-x^{-1}\right) e^{\left(x+x^{-1}\right)} d x=f(x)+C$, then $f(1)-f(-1)=$

$ \int \frac{1}{x^{m} \sqrt[m]{x^{m}+1}} d x =$

If $\int(\sqrt{\operatorname{cosec} x+1}) d x=k \tan ^{-1}(f(x))+C$, then $\frac{1}{k} f\left(\frac{\pi}{6}\right)=$

$\int \sqrt{4 \cos ^2 x-5 \sin ^2 x} \cos x d x=$