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Did I do this properly? Integration by Partial Fractions

  • Thread starter the7joker7
  • Start date
113
0
1. Homework Statement

Evaluate the indefinite integral.

int (6 x + 7)/(x^2 + 1) dx `

3. The Attempt at a Solution

A/(x + 1) + B/(x - 1)

6x + 7 = A(x - 1) + B(x + 1)

6x + 7 = (A + B)x + (-A + B)

A + B = 6

-A + B = 7

A + (7 + A) = 6

2A = -1.

A = -.5

B = 3.5

So the answer should be...

-.5ln(x + 1) + 3.5ln(x - 1) + C

Is this correct?
 

Answers and Replies

1,750
1
Differentiate your anti-derivative and see if it becomes your original Integral.

Also, I don't think it is. How did you break ... [tex]x^2+1[/tex] ???

You don't need to use Partial Fractions.

[tex]\int\frac{6x+7}{x^2+1}dx[/tex]


[tex]\int\left(\frac{6x}{x^2+1}+\frac{7}{x^2+1}\right)dx[/tex]
 
Last edited:
113
0
-.5(1/x + 1) + 3.5(1/x - 1)

Blah. =/

What did I do wrong?
 
1,750
1
Looking at your work ... looks like you broke [tex]x^2+1[/tex] to [tex](x+1)(x-1)[/tex]

Yes?

[tex]x^2-1=(x+1)(x-1)[/tex] so ... [tex]x^2+1\neq(x+1)(x-1)[/tex]
 

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