## ksaimouli Group Title by partial frac one year ago one year ago

1. ksaimouli Group Title

$\int\limits_{}\frac{ 2x^3 }{ x^2-4 }$

2. ksaimouli Group Title

i should do the long division right

3. ksaimouli Group Title

i got $x^2-4+\frac{ 8x }{ 2x }$

4. ksaimouli Group Title

@zepdrix

5. SithsAndGiggles Group Title

You're right about doing long division first, but it doesn't look like you did it right.

6. ksaimouli Group Title

|dw:1361917090294:dw|

7. SithsAndGiggles Group Title

|dw:1361917028271:dw|

8. SithsAndGiggles Group Title

Right, so by long division you get $2x+\frac{8x}{x^2-4}$

9. ksaimouli Group Title

so should i make the whole function as|dw:1361917417172:dw|

10. SithsAndGiggles Group Title

You can, but that doesn't mean you should. Your integral has changed from $\int\frac{2x^3}{x^2-4}dx$ to $\int\left(2x+\frac{8x}{x^2-4}\right)\;dx$ Integrate term by term, with partial fraction decomp on the second term.

11. ksaimouli Group Title

right here i could use u substitution right

12. SithsAndGiggles Group Title

Or that, yes. A sub might actually shorten the work, so I'd suggest that.

13. ksaimouli Group Title

i got $x^2+4\ln(x^2-4)$

14. ksaimouli Group Title

+C

15. ksaimouli Group Title

is this right @SithsAndGiggles

16. SithsAndGiggles Group Title

Yes that's right, though I would replace the parentheses with absolute value bars.

17. ksaimouli Group Title

ya i dont know how to use that in equation so put the ()

18. ksaimouli Group Title

thx

19. SithsAndGiggles Group Title

You're welcome. By the way, absolute value bars are above the Enter/Return key. Hold shift and click the backslash (\) button to get (|)

20. ksaimouli Group Title

|2x+1|

21. ksaimouli Group Title

ya i got that thx