I\'m a little stuck and confused on this. Calculate the integral below by partia

Question

I'm a little stuck and confused on this. Calculate the integral below by partial fractions and by using the indicated substitution. Be sure that you can show how the results you obtain are the same. Integral of 2x/(x^2-9) First, rewrite this with partial fractions: integral (a)______dx + integral (b)________ dx. = (c)__________ + (d)_________+C (Note that you should not include the in your entered answer, as it has been provided at the end of the expression.) Next, use the substitution [w=x^2-9] to find the integral: . e)______dw = (f)__________ + C = (g)__________ (For the second answer blank, give your antiderivative in terms of the variable . Again, note that you should not include the in your answer.) My correct answers are as follows: a) (1/x+3) b) (1/(x-3) c) ln(x+3) d) --> I had ln(x-3), but it said that was incorrect. e) 1/w f) --> I had ln (w), but it said that was incorrect g) ---> I had 1/(x^2-9), but it said that was incorrect.

Explanation / Answer

f 2x/(x^2-9) First, rewrite this with partial fractions:

f(x) = 2x/ (x+3) (x-3)

2x/(x+3)(x-3) = A/(x+3) + B(x-3)

2x = A(x-3) +B (x+3)

let x = 3

6B = 2*3 =6

B = 1

A = 1

integral (a)___(1/(x+3)___dx + integral (b)__1/(x-3)______ dx. =

(c)__ln|x+3|________ + (d)__ln|x-3|_______+C

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