3.3 Trigonometric Substitution

[STARTS AT 28:08]

Instructor: Number 40. Rewrite this using tangent as a substitution and don't evaluate. This is kind of like that last one we did with sine. And actually, we want to use tangent, or 2 tangent theta, for that. Because our a value is 4. So this is going to be x cubed. So that would be 8-- tangent cubed theta, square root of 4 tangent squared theta plus 4, which will become a 2. I'll leave this part here-- this will become a 2 tangent theta plus 1. So that'll be a secant. 

And we need our d theta actually. So we should have had a d theta, or dx becomes 2 secant squared theta. So 2 secant squared theta d theta. So then we've got another secant squared, which will become a secant cubed. So we have the integral of that will be 32. We have a tangent cubed theta. And then, we have a secant cubed theta, d theta. 

[ENDS AT 29:57]