Question

How do you integrate: (3t^2+t+4)/t^3+t

Answer 1

\[\int\limits_{1}^{\sqrt{3}}\frac{ 3t^2+t+4 }{ t^3+t }dt\]

Answer 2

Correctly? What's Partial your Fraction plan?

Answer 3

I tried breaking it apart for integration by parts, tried u sub, none of it is working

Answer 4

Ill show you what I did

Answer 5

factor out a t from the denomiator
\[\frac{ A }{ t } + \frac{ Bx+C }{ t^2+1 } = 3t^2...\]

Answer 6

Of course, abb0t means \(Bt + C\). In any case, you'll probably have to cut this up after the partial fractions. \(\dfrac{Bt}{t^{2}+1} + \dfrac{C}{t^{2}+1}\). Now, THERE's your ArcTangent.

Answer 7

One degree less than the denominator. Since the denominator cannot be factored, it is what it is.

Answer 8

That's it. One degree less than the degree of the denominator, Excellent thinking it through!

Answer 9

I still do not get this.
My class notes say, If x^2+bx+c is an irriducible quad. factor of q(x) and (x^2+bx+c)^n, the highest power dividiing of q(x). To this factor, assign the sum of n partial fractions. Repeat for each irriducible factor.
This makes zero sense to me. Can you please help translate it for me. Then maybe I can figure out how to actually do it, because I am stuck

Answer 10

I can't really help you to sort through that.

Answer 11

To you tube I go....

Answer 12

still need help with your class notes ? i may be able to explain it with an example...

Answer 13

I can help drive this home.