As a weird example, consider the weird integral:1e2x-12dxThis is actually a very specific u-substitution for arcsec(u(x))! But what's our u? Let usgo through this piece bypiece:We recall that our arcsec derivativeintegral formula isof the form:ddxarcsec(u(x))=u'(x)|u(x)|(u(x))2-12Now suppose that u(x)=ex, this would mean that our derivative expression would look like:ddxarcsec(ex)=Because ex,0 for all x,we can conclude that |ex|,ex.Cancelling out the now common factor in our revised expression, and simplifying the exponent in the square root,we can simplify our derivative as:ddxarcsec(ex)=And sowe now know that: 1e2x-12dx=,+C