3.6 Integrals 501 to 507

\(\int \genfrac {}{}{}{}{x^2}{(1+x)^{5/2} (1-x+x^2)^{5/2}} \, dx\) [501]
\(\int \genfrac {}{}{}{}{x}{(1+x)^{5/2} (1-x+x^2)^{5/2}} \, dx\) [502]
\(\int \genfrac {}{}{}{}{1}{(1+x)^{5/2} (1-x+x^2)^{5/2}} \, dx\) [503]
\(\int \genfrac {}{}{}{}{1}{x (1+x)^{5/2} (1-x+x^2)^{5/2}} \, dx\) [504]
\(\int \genfrac {}{}{}{}{1}{x^2 (1+x)^{5/2} (1-x+x^2)^{5/2}} \, dx\) [505]
\(\int \genfrac {}{}{}{}{1}{x^3 (1+x)^{5/2} (1-x+x^2)^{5/2}} \, dx\) [506]
\(\int \genfrac {}{}{}{}{1}{\sqrt {1-\genfrac {}{}{}{}{1}{c^2 x^2}} x^2 \sqrt {d+e x}} \, dx\) [507]