3.1 Integrals 1 to 6

\(\int \genfrac {}{}{}{}{-32+36 x-42 x^2+21 x^3-10 x^4+3 x^5}{x (1+x^2) (4+x^2)^2} \, dx\) [1]
\(\int \genfrac {}{}{}{}{x^2 (A+B x^2)}{\sqrt {a+b x^2} (c+d x^2)^{3/2}} \, dx\) [2]
\(\int \genfrac {}{}{}{}{x^2 (A+B x^2)}{\sqrt {a+b x^2} (c-d x^2)^{3/2}} \, dx\) [3]
\(\int \genfrac {}{}{}{}{x^2 (A+B x^2)}{\sqrt {a-b x^2} (c+d x^2)^{3/2}} \, dx\) [4]
\(\int \genfrac {}{}{}{}{x^2 (A+B x^2)}{\sqrt {a-b x^2} (c-d x^2)^{3/2}} \, dx\) [5]
\(\int x^m (A+B x^2+C x^3) (a+b x^n)^p (c+d x^n)^q \, dx\) [6]