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## baldymcgee6 Group Title How to setup this integral with partial fractions..? one year ago one year ago

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1. baldymcgee6 Group Title

|dw:1358744328225:dw|

2. baldymcgee6 Group Title

x^7

3. baldymcgee6 Group Title

just have to set it up, don't have to actually integrate it. :)

4. hartnn Group Title

x(x^6-1) =x(x^3+1)(x^3-1)

5. baldymcgee6 Group Title

$\LARGE{\int\limits \frac{ 1 }{ x^7 - x }dx}$

6. kirbykirby Group Title

|dw:1358744642346:dw|

7. hartnn Group Title

do you know general formulas for a^3+b^3 and a^3-b^3..

8. baldymcgee6 Group Title

yes

9. baldymcgee6 Group Title

so how would this spit into partials?

10. hartnn Group Title

if there is quadratic equation in denominator, which cannot be factorized, then in numerator, it'll be linear expression, Ax+B...

11. kirbykirby Group Title

For x^3-1 and x^3+1 you can use Long polynomial division by finding a factor (x-a) where a is a root of the polynomial

12. hartnn Group Title

so, whats x^3+1=... ? x^3-1=.... ?

13. kirbykirby Group Title

I never learnt the general formula for a^3+b^3. I think it's easier to do polynomial division because it will work for higher powers

14. baldymcgee6 Group Title

x^3 +1 = (x+1)(x^2-x+1)

15. hartnn Group Title

so, above x^2-x+1 will come a linear expression like Ax+B and above linear terms like x, x(x+1), constants like C,D,E ... will come.

16. baldymcgee6 Group Title

@kirbykirby polynomial division of what and what?

17. baldymcgee6 Group Title

x^3 -1 = (x-1)(x^2+x+1)

18. baldymcgee6 Group Title

okay, i'll try this

19. hartnn Group Title

so, you have 5 factors, out of which 2 is quadratic.

20. kirbykirby Group Title

for x^3+1, you find the factors of the constant (here, its 1) and find which one = 0 when you plug it into your x-terms. So, -1 works: ((-1)^3+1) = 0. So, the factor that divides the polynomial is always of the form (x-a). So, (x-(-1)) = (x+1). Then divide x^3+1 into x+1

21. baldymcgee6 Group Title

|dw:1358745155474:dw|

22. hartnn Group Title

$$\checkmark$$

23. baldymcgee6 Group Title

@kirbykirby that is useful to know rather than memorizing these formulas.

24. baldymcgee6 Group Title

thanks for the help guys!

25. kirbykirby Group Title

No problem :)

26. kirbykirby Group Title

It's often called the "Factor Theorem". http://en.wikipedia.org/wiki/Factor_theorem