Consider the integral ∫−sin⁡(y)cos⁡(y)+7 dy\displaystyle \int\frac{{-{\sin{{\left({y}\right)}}}}}{{{\cos{{\left({y}\right)}}}+{7}}}\ {\left.{d}{y}\right.}:

This can be transformed into a basic integral by letting

u=\displaystyle {u}=   and

du=\displaystyle {d}{u}= dy\displaystyle {\left.{d}{y}\right.}  

After performing the substitution, you obtain the integral

∫\displaystyle \int du\displaystyle {d}{u}  

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