Some partial fraction problems.

[LostInCalculus]

I am having problems with a few questions, I figured I had them right but inputing them comes back with them being incorrect.

1) Integral of 2x^3-4x^2+16 / x^4+2x^3

I factored the bottom into x^3(x+2) and used A/x +B/x^2+C/x^3+d/(x+2) for partial fractions and solved for A, B, C, and D.

I got A=0, B=-4, C=8, and D=2

So I end up with Int -4/x^2 + Int8/x^3 + Int 2/(x+2)

I solved those and got 4/x - 4/x^2 + 2ln(x+2) I figured that was the answer but it comes back as wrong.



2) An early question broken into parts, I got everything right up to A/x+1 + Bx+C/x^2+4 with A=2, B=-4, and C=0.

So I know the intrgral I need to solve is 2/x+1 - 4x/x^2+4

The natural log rule makes integrating the first part 2ln(x+1)

The second part I used u=x^2+4 du=2x so x=du/2 taking the -4 out of the integral I have x/x^2+4, which is 1/2 du/u, which is 1/2ln(u), and 1/2ln(x^2+4). So taking the initial -4 times the 1/2 that leaves that integral being -2ln(x^2+4)

So for a total answer I got 2ln(x+1) - 2ln(x^2+4).

It came back as wrong, I am stumped on it.

3) Integral of -5x^3 - 2x^2 + 0 / x^4 +0x^3

I figure this is just -5x^3 - 2x^2 / x^4 as the 0 terms should be moot.

So I solved it using partial fractions A/x + B/x^2 + C/x^3 +D/x^4

Solving for those I got A=-5 B=-2 C=0 and D=0

So you are left integrating -5/x - 2/x^2

I got -5ln(x) + 2/x I cannot see where I went wrong getting to that point.

If anyone can help out with these questions I would be most grateful. I am stumped

 

[galactus]

I am having problems with a few questions, I figured I had them right but inputing them comes back with them being incorrect.

1) Integral of 2x^3-4x^2+16 / x^4+2x^3

I solved those and got \(\displaystyle \frac{4}{x} - \frac{4}{x^{2}} + 2ln(x+2)\) I figured that was the answer but it comes back as wrong.

That is correct. Who said it wasn't?. Let me guess...an infernal computer.

 

[galactus]

All of your problems check as correct. The second one could be written as \(\displaystyle 2ln(\frac{x+1}{x^{2}+4})\), but that's nitpicking. If this is a computer telling you they're wrong, then who knows what's the matter.

 

[LostInCalculus]

It is indeed a computer

 

[galactus]

Computer tests are fine if it is multiple choice, but they can be mighty temperamental if you have to enter in your answer. Especially, in a calc class.

 

[Dr. Flim-Flam]

Note: If you have a TI-89, then expand((2x^3-4x^2+16)/(x^4+2x^3),x) = 2/(x+2)-(4/x^2)+8/x^3.

expand is F2-3 Says a lot of grunt work and always works.