Partial Fractoin Integration Check

[Procrastinate]

Partial Fraction Integration Check

Hello, I was just wondering whether my answer for my partial fraction integration question was right. Attached are three pages of my working but the answer is at the bottom of the third page (027) and the question is at the top of the first page (025).

Thanks.

 

[Mentallic]

You have a mistake, give me a second to pinpoint where it is.
Oh and by the way, you integrated the fraction at the end with the squared denominator wrong.

$$\int \frac{1}{x^2}dx=\frac{-1}{x}$$

 

[Mentallic]

Ok your arithmetic was wrong when you substituted x=-1/3.

 

[Procrastinate]

Ok your arithmetic was wrong when you substituted x=-1/3.

Ok. I fixed that up (as well as my other small integration error.)

My final answer is now:

$$\frac{22}{25}\ln|x+2|+-\frac{4}{5(x+2)}+-\frac{2}{75}\ln|3x+1| + C$$.

Is this correct?

 

[Mentallic]

The ln(3x+1) term is incorrect. I get -16/75 as the constant multiplier.

 

[Procrastinate]

Oh yes, that is right. I just accidentally copied it down wrong. Thanks for your help.

 

[Procrastinate]

The ln(3x+1) term is incorrect. I get -16/75 as the constant multiplier.

$$\frac{22}{25}\ln|x+2|+-\frac{4}{5(x+2)}+-\frac{16}{75}\ln|3x+1| + C$$

 

[Mentallic]

No problem