Integration by Substitution

[irishpump]

t^2/(t^3-2)^5 dt Find each indefinite integral and check the result by differentiating.

I am totally stumped. I thought I knew what I was doing when it comes to anti-derivatives, which we just recently started learning. I got this as a practive problem, but even when I look at the 6 substitution formulas, I'm not sure what one would work. I thought I'd just try to work it out, but I can't seem to figure out how to even set this up. According to my book, the answer is:

-1/12(t^3 - 2)^-4 + C

Just trying to work backwards after noting the answer I still can't figure out how this problem works and again how to set it up.

Again, thanks for any and all help! Very very much appreciated!

 

[srmichael]

t^2/(t^3-2)^5 dt Find each indefinite integral and check the result by differentiating.

I am totally stumped. I thought I knew what I was doing when it comes to anti-derivatives, which we just recently started learning. I got this as a practive problem, but even when I look at the 6 substitution formulas, I'm not sure what one would work. I thought I'd just try to work it out, but I can't seem to figure out how to even set this up. According to my book, the answer is:

-1/12(t^3 - 2)^-4 + C

Just trying to work backwards after noting the answer I still can't figure out how this problem works and again how to set it up.

Again, thanks for any and all help! Very very much appreciated!

General rule of thumb that works most times is to let u = "the stuff in the parenthesis". Start with that and then come back to us if you get stuck.