I wrote this set of exercises for my students so they could practice recognizing when to do a substitution versus when to just use some algebra (long division, completing the square, expanding a binomial, etc.) or an inverse trig function as part of the integration process. This circuit contains 22 indefinite integrals that are all "rational" in form. I have been intentional in my choices and made many of the integrands extremely similar. Questions 21 and 22 require the method of partial fractions, but at that point in the circuit students can work backwards from the remaining answers by taking the derivatives.
There is no answer key included with this download since the answers are imbedded in the circuit. The teacher must work the problems ahead of time to decide how to best use this resource with his or her students. My colleagues and I check our work carefully, however, if you suspect there is an error (or if you get stuck), please email me at email@example.com.