"An old saying goes, 'The first step in making rabbit stew is to catch a rabbit.' Likewise, the first step in integrating by substitution is to find a suitable change of variable u=u(x) that simplifies the integrand of the given integral ~f(x)dx without adding undesired complexity when dx is replaced by du=u'(x) dx."
Ouch. I think I just got kicked in the brain.
My initial reaction was: At least they tried. They're no storybook writers, they're mathematicians trying to write a somewhat interesting textbook.
But upon further reflection, I know that this was actually meant as a jab to all the writers and artists and poets who read this textbook, whose eyes glaze over and hearts sink as they realize they're denying themselves and enduring the crucifixion of all humanity that is Calculus. They've caught us by the leg. The broth is boiling.
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