$\int \sqrt{\frac{1+x}{1-x}} \, dx = $

$\int_{\frac{1}{\sqrt[5]{31}}}^{\frac{1}{\sqrt[5]{242}}} \frac{1}{\sqrt[5]{x^{30}+x^{25}}} d x=$

$\int \frac{dx}{\tan x+\cot x+\sec x+\operatorname{cosec} x} = $

$\int \sqrt{\frac{2+x}{2-x}} \, dx$ is equal to

$\int \frac{\sqrt{\cos 2 x}}{\sin x} d x=$

If $\int(\sin x )^{\frac{-11}{2}}(\cos x )^{\frac{-5}{2}} dx = -\frac{p_1}{q_1}(\cot x)^{\frac{9}{2}}-\frac{p_2}{q_2}(\cot x)^{\frac{5}{2}}-\frac{p_3}{q_3}(\cot x)^{\frac{1}{2}}+\frac{p_4}{q_4}(\cot x)^{\frac{-3}{2}}+C,$ where $p_i$ and $q_i$ are positive integers with $\operatorname{gcd}(p_i, q_i)=1$ for $i =1,2,3,4$ and $C$ is the constant of integration, then $\frac{15 p_1 p_2 p_3 p_4}{q_1 q_2 q_3 q_4}$ is equal to . . . . . . .