## sat_chen 2 years ago Partial integration question

1. sat_chen

hold on i didnt know you couldnt post pic from iphone jsut 1 sec

2. hartnn

draw your question, maybe...

3. sat_chen

i have done a lot of the steps so just 1 sec

4. sat_chen

but heres the question |dw:1359962006954:dw|

5. hartnn

that will be pretty exhausting..

6. hartnn

x^4 (x+3) A/x+B/x^2+C/x^3+D/x^4 +E/(x+3)

7. sat_chen

8. sat_chen

do you see my steps ill try posting another pic

9. hartnn

yes, D=1, E=4 are correct.

10. sat_chen

yea i got that far phew but how do i solve for the A B and C after that?

11. hartnn

you'll need to put 3 different values of x say x=1,-1,2 then you get 3 equations in A,B, C with 3 unknowns...

12. sat_chen

can you show me what you mean i dont get what you mean by that

13. sat_chen

should really have listened in my algebra classes sorry :(

14. hartnn

\(Ax^3(x+3)+Bx^2(x+3)+Cx^3(x+3)+(x+3)+4x^4\\ =9x^4+17x^3+3x^2-8x+3\) put x = 1, to get 1 equation in A,B, C

15. sat_chen

it should be Cx (x+3)

16. hartnn

another method is comparing the co-efficients to get 3 equations... yes, typo...it should be Cx(x+3)

17. hartnn

like co-efficient of x^4 will be A+4 and no right side, its 9 so, A+4= 9 gives A=5

18. hartnn

i think you should proceed with comparing the co-efficients..

19. sat_chen

so if you plug in x = 1 you get 4A + 4B+ 4C = 16

20. hartnn

i think comapring the co-efficients will give you answer much faster, if you have understood it.

21. sat_chen

sorry internet disconnected agian

22. hartnn

co-efficient of x^3 = 3A+B = 15+B on left on right its 17 so, 15+B = 17 gives B=3

23. hartnn

24. sat_chen

ok so what you are saying is that for A you A + 4 = 9 then for B would you B + 3 =17 then for C would you C + 2 =3

25. sat_chen

where did you get the|dw:1359963485018:dw|

26. hartnn

it should be B+3A =17

27. sat_chen

then i also guess i dont get how you got the A + 4 either because my logic was wrong

28. hartnn

|dw:1359963578884:dw|

29. sat_chen

not getting the |dw:1359963731639:dw|

30. hartnn

\(Ax^3(x+3)+Bx^2(x+3)+Cx(x+3)+(x+3)+4x^4\\ =9x^4+17x^3+3x^2-8x+3 \\ ~ \\Ax^4+3Ax^3 +Bx^3+3Bx^2+Cx^2+3Cx+x+3+4x^4= \\ =9x^4+17x^3+3x^2-8x+3\)

31. sat_chen

do you have a formula or something that tells us that or how does that work?

32. hartnn

\(Ax^3(x+3)+Bx^2(x+3)+Cx(x+3)+(x+3)+4x^4\\ =9x^4+17x^3+3x^2-8x+3 \\ ~ \\Ax^4+3Ax^3 +Bx^3+3Bx^2+Cx^2+3Cx+x+3+4x^4= \\ =9x^4+17x^3+3x^2-8x+3 \\ ~ \\ (A+4)x^4+(3A+B)x^3+....=...\)

33. hartnn

comapring the c-efficiens on left and right, A+4=9 3A+B=17 did you get this ?

34. sat_chen

its not showing it in nice formatting so im writing it down just 1 sec

35. hartnn

Ax^3(x+3)+Bx^2(x+3)+Cx(x+3)+(x+3)+4x^4=9x^4+17x^3+3x^2−8x+3 Ax^4+3Ax^3+Bx^3+3Bx^2+Cx^2+3Cx+x+3+4x^4=9x^4+17x^3+3x^2−8x+3 (A+4)x^4+(3A+B)x^3+....=9x^4+17x^3+...

36. hartnn

i just combined like terms on left..