3.1 Integrals 1 to 13

\(\int \genfrac {}{}{}{}{\sqrt {1+2 x+x^2}}{\sqrt {1+x^2}} \, dx\) [1]
\(\int \genfrac {}{}{}{}{1}{(1-x^2) (a+b x+c x^2)} \, dx\) [2]
\(\int \genfrac {}{}{}{}{1}{(1-x) (1+x) (a+b x+c x^2)} \, dx\) [3]
\(\int \genfrac {}{}{}{}{(a+2 b x-a x^2)^4}{(-1+x^2)^5} \, dx\) [4]
\(\int \genfrac {}{}{}{}{\sqrt {d+e x+f x^2}}{(a+c x^2)^2} \, dx\) [5]
\(\int \genfrac {}{}{}{}{1}{(-1+x^2)^2 \sqrt {-1+x+x^2}} \, dx\) [6]
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b x+c x^2} \sqrt {d+f x^2}} \, dx\) [7]
\(\int (a+b x+c x^2)^3 (d+f x^2)^q \, dx\) [8]
\(\int (a+b x+c x^2)^2 (d+f x^2)^q \, dx\) [9]
\(\int (a+b x+c x^2) (d+f x^2)^q \, dx\) [10]
\(\int (d+f x^2)^q \, dx\) [11]
\(\int \genfrac {}{}{}{}{(d+f x^2)^q}{a+b x+c x^2} \, dx\) [12]
\(\int \genfrac {}{}{}{}{(d+f x^2)^q}{(a+b x+c x^2)^2} \, dx\) [13]