Page 24 - Calculus for the Clueless

Example 4—

At this point you might say, ''This doesn't do anything for us." You'd be right. Let's do it again. We let U = e 5x
because, if we reversed, we would wind up with the original integral and would have accomplished nothing. dV
= sin 3x dx. V = (-cos 3x)/3. (Note that, in the third line, the product of three minus signs is a minus.)

It looks like we will be going forever. However, notice that the original integral and the last integral are the
same except for a constant. Call the original integral I (for integral, of course). The last line becomes

now I = (9/9)I

so

Note