I have to integrate this question and show my substitutions. My question is integral 2/(t^3-4t) dt to start this question do I move the bottom to the top? and make it to the ^-1?

Question

I have to integrate this question and show my substitutions.  My question is integral 2/(t^3-4t) dt to start this question do I move the bottom to the top? and make it to the ^-1?

agreene · Answer

I would start by factoring out the 2, and then use partial fractions...

anonymous · Answer

there is only a 2 on the top. I can factor a t from the bottom

agreene · Answer

the 2 is a constant.

anonymous · Answer

I was thinking of putting integral 2(t^3-4t)^-1 dt? I really struggle with this stuff

agreene · Answer

$$\int \frac{2}{t^3-4t}dt=2\int\frac{1}{t^3-4t}dt$$

anonymous · Answer

oh yeah forgot about the constant.

agreene · Answer

$$2\int (-\frac{1}{4t}+\frac{1}{8(t+2)}+\frac{1}{8(t-2)})dt$$
from partial fractions,
from there I would split into the 3 different fractional integrands and go from there--they look fairly easy. Of course, if you haven't learned partial fractions--probably not the best idea to use it, lol... but, thats where my mind goes when I see this type of question.

anonymous · Answer

no we have not learned partial fractions that is next on the agenda.

anonymous · Answer

all the examples we have are involving NON fractions thats why having trouble.

agreene · Answer

hrm, honestly I'm not sure how to do this without using partial fractions....

anonymous · Answer

hmmm... maybe I will read ahead then and see how to do partial fractions then.  You are obviously very intelligent.  thanks :)