(secx)^2 sqrt((tanx)^3)dx
x^3/sqrt(x^2+25)
Integral from 3 to sqrt(24) of x/sqrt(x^2-8)
Integral from 1/2 to 5/2 of 1/sqrt(6x+1)
I don't get any of this.. I have a test of this Tuesday and still have no idea how to do it..
(secx)^2 sqrt((tanx)^3)dx
x^3/sqrt(x^2+25)
Integral from 3 to sqrt(24) of x/sqrt(x^2-8)
Integral from 1/2 to 5/2 of 1/sqrt(6x+1)
I don't get any of this.. I have a test of this Tuesday and still have no idea how to do it..
The concept for most of these is all based on the Chain Rule: . So now doesn't it make sense that ?
So lets take your first one
The key here is to identify your . The first thing you should notice is that . So now let us rewrite this as . The next step is to identify our since we have that our it makes sense that . So now let us rewrite our integral as . From here we see that so . So by the fact that we can see that . Now that was a lot of work wasn't it? There is a method that makes this much easier it is called u-substitution. It basically say that if I have why not let ...but I have only replaced half of my "symbols" in the integral. What about ? We take care of this by noting that if . So after our substitution our integral becomes which usually makes this much easier. So in the previous example had we let our integral would have been transformed into which is pretty easy. Most of the ones you have here are of the form ...see if you can find them and then see if you can do them. The ones that aren't should be apparent...ask back later for more help on those.