Integral of (3x+1)/(x^3(3x+2)(x-1))

Question

myininaya · Answer

partial fractions is needed here

myininaya · Answer

hint
$$\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x^3}+\frac{D}{3x+2}+\frac{E}{x-1}$$

anonymous · Answer

What do you do with all of that? I see that, in my notes, it adds up all of that using cross multiplication. But how do you do that with 5 fractions?

myininaya · Answer

it is suppose to equal $$\frac{3x+1}{x^3(3x+2)(x-1)}$$
to find when that sum of fractions equal the one in your integral you need to find a common denominator so you can write the fractions as one

myininaya · Answer

$$\frac{A}{x} \cdot \frac{x^2(3x+2)(x-1)}{x^2(3x+2)(x-1)}$$
for example the first fraction needs to be multiplied by this 1
can you do the others?

anonymous · Answer

Thank you, I think I got it from here!

myininaya · Answer

Ok it isn't that bad
I know it seems a little long
and maybe it would be too long if it was a test (maybe)

anonymous · Answer

Its homework... this teacher has a knack for making things look super complicated. Thanks a bunch