<p>we covered trig substitution quite heavily in my bc class. kinda tedious, but a useful skill :)</p>
<p>u substitution? That's just substitution. I'm talking x=tan (t/2)...</p>
<p>Yeah, Stewart doesn't cover it. It's one of the many reasons why I don't like that book.</p>
<p>Sorry, I meant t=tan(x/2). Silly dummy variables.</p>
<p>/it's "magical" because it appears to come out of nowhere. I guess "pulled-out of your (rear-end)" substitution doesn't sound so nice.</p>
<p>I looked at it for a little bit, but it was late and I was like, no way am I getting this down. Everything is about the magic triangles.</p>
<p>Do you know how to get the taylor expansion for sin-1(x). I tried getting it, but I dont know how.</p>
<p>check out section 3.4 here:</p>
<p>"U substitution, integration by parts, integration by partial fractions, and trig substitutions (may not be covered)" My calculus BC class covered these but they were not collectively called "magic substitution". The class also covered hyperbolic integration/differentiation and integration by borrowing. Integration by borrowing is used to integrate y=x*e^(x^2) and similar equations.</p>
<p>For the trig substition, are you talking about integrating x^3/root(1-x^2) by plugging in that x=sin(theta)
yields integral of sin^3 cos / root(10sin^2) and then agter you plug back in for cos. It doesnt seem that bad, but I just wonder if this sub is actually covered, because to some trig might mean cos = root(1-sin^2) and stuff.</p>