<p>We're doing substitutions in my class for integrals and I understand the whole general concept. The problem is my teacher doesn't know how to do a lot of these herself and just leaves an answerbook at the top of her desk for people to look at when they don't understand something.</p>
<p>Right now I have these problems where the dx is in the numerator...and I have no idea how to go about doing this after a certain point. Can someone help me?</p>
<p>I don't understand these three types of problems.</p>
<p>dx/sin^23x </p>
<p>dx/x+2 with an upper limit of 7 and lower limit of 0</p>
<p>Well the first question it looks like you need to do integration by parts. Also, to make the questions look more familiar, I would get it out of the fraction. For example, for the second question, instead of making it dx/x+2, I would make it (x+2)^-1 dx. It makes it easier to figue out what to make u.</p>
<p>Whenever you have a dx in the numerator, you can simply pull it to the outside of a fraction, so dx/sin^23x = 1/(sin x)^23 dx.</p>
<p>Are you sure you don't have a cos x in the integral of this last case? By parts would be ugly, and is pretty atypical for the quesitons in this section. Or did you mean (sin 3x)^2 perhaps?</p>