3.1 Integrals 1 to 5

\(\int \genfrac {}{}{}{}{(e+f x)^3 \sqrt {c+d x^3}}{a+b x^3} \, dx\) [1]
\(\int (a+b x^3)^p (c+d x^3)^q (a A c+A (b c (1+3 (1+p))+a d (1+3 (1+q))) x^3+A b d (1+3 (2+p+q)) x^6) \, dx\) [2]
\(\int \genfrac {}{}{}{}{A+B x^3+C x^6+D x^9}{\sqrt [3]{a+b x^3} (e+f x^3)} \, dx\) [3]
\(\int \genfrac {}{}{}{}{A+B x^n+C x^{2 n}}{\sqrt {a+b x^n} (e+f x^n)} \, dx\) [4]
\(\int (a+b x^n)^p (c+d x^n)^q (a A c+A (b c (1+n (1+p))+a d (1+n (1+q))) x^n+A b d (1+n (2+p+q)) x^{2 n}) \, dx\) [5]