Most techniques involving complex functions are designed to replace complex parts of the function with simpler expressions that can be solved by using the 'standard' rules of integration. In some cases, multiple approaches need to be used. This examples illustrates how Integration by Parts can be combined with the Substitution of Variables approach to evaluate a complex function:
$\int arctan\phantom{\rule{3px}{0ex}}x\phantom{\rule{5px}{0ex}}dx$
Combining Integration by Parts with Substitution