(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

So I am trying to integrate the following. I believe I have to use partial fractions.

[itex]\frac{1}{(x+4)^{2}(x-3)}[/itex]

2. Relevant equations

3. The attempt at a solution

So I am trying to expand the above into something that I can integrate. So I equated the integrand with the following:

integrand = [itex]\frac{A}{(x-3)}[/itex]+[itex]\frac{Bx+C}{(x^{2}+16+8x) <--just the expanded form of (x+4)^{2}}[/itex]

So by creating a common denominator you get

1= A(x[itex]^{2}[/itex]+16+8x)+(Bx+C)(x-3)

By inputing x=3 first, I solve for A=1/49

Then by imputing x=0 I get C=-33/49

And then by imputing x=1 I get B=-45/49

So plugging that into the original, I get:

integrand = [itex]\frac{1}{49(x-3)}[/itex]-[itex]\frac{(45/49)x-(33/49)}{(x+4)(x+4)}[/itex]

When I check my answer by plugging a random value of x into the integrand, and then into the RHS, I find that they are not equal. Where did I mess up?

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# What is wrong with this method? (partial fractions)

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