Consider the integral ∫−tan⁡(θ)⋅ln⁡(7cos⁡(θ)) dθ\displaystyle \int-{\tan{{\left(\theta\right)}}}\cdot{\ln{{\left({7}{\cos{{\left(\theta\right)}}}\right)}}}\ {d}\theta:

This can be transformed into a basic integral by letting

u=\displaystyle {u}=   and

du=\displaystyle {d}{u}= dθ\displaystyle {d}\theta  

After perfroming the substitution, you obtain the integral

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

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