What should you do when your rational integrand is not of the form du/u? You could try to complete the square on the denominator, which leads us neatly into our second objective. Duration: 7:06

As the previous example illustrated, completing the square often leads to an antiderivative involving an inverse trig function. It would be nice if we had a foolproof antiderivative rule for this type of problem. Here, let's make one. Duration: 5:28

While Example 10 gives us a novice-level application of our new antiderivative rule for arctan, Example 11 promises to increase the complexity somewhat by requiring the completion of a square. Duration: 5:19

For challenge and enjoyment, why don't we combine both of the techniques learned in this lesson into one slightly intimidating problem? Why, indeed. Duration: 16:11