3.1 Integrals 1 to 6

\(\int \genfrac {}{}{}{}{1}{\sqrt {-1-\sqrt {x}} \sqrt {-1+\sqrt {x}} \sqrt {1+x}} \, dx\) [1]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a-b \sqrt {x}} \sqrt {a+b \sqrt {x}} \sqrt {a^2+b^2 x}} \, dx\) [2]
\(\int (a-b x^n)^p (a+b x^n)^p (c+d x^{2 n})^q \, dx\) [3]
\(\int (a-b x^n)^p (a+b x^n)^p (a^2+b^2 x^{2 n})^p \, dx\) [4]
\(\int \genfrac {}{}{}{}{(c+d x^{2 n})^p}{(a-b x^n) (a+b x^n)} \, dx\) [5]
\(\int (a-b x^{n/2})^p (a+b x^{n/2})^p (\genfrac {}{}{}{}{a^2 d (1+p)}{b^2 (1+\genfrac {}{}{}{}{-1-2 n-n p}{n})}+d x^n)^{\genfrac {}{}{}{}{-1-2 n-n p}{n}} \, dx\) [6]