Integration involving partial fraction

[appplejack]

Homework Statement

I want to check the answer to this question.

⌠ 2 x dx / (x+1) (x+2)
⌡ 1

Homework Equations

The Attempt at a Solution

For partial fraction I got A= -1 and B = 2

My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3

 

[RoshanBBQ]

Homework Statement

I want to check the answer to this question.

⌠ 2 x dx / (x+1) (x+2)
⌡ 1

Homework Equations

The Attempt at a Solution

For partial fraction I got A= -1 and B = 2

My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3

There is a more important question at hand. Do you understand the order of operations?

 

[appplejack]

There is a more important question at hand. Do you understand the order of operations?

Yes. I just need to check the answer.

 

[RoshanBBQ]

Yes. I just need to check the answer.

Judging by your problem statement, I can't be too sure.

Also, are you sure ln(a) + ln(b) = ln(a)ln(b)?

 

[scurty]

My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3

This line doesn't make any sense to me. :/ Regardless, the answer is incorrect on the left hand side. Show us what integral you got when you split the partial fraction up (A=-1 and B=2 doesn't mean much if we don't know what term they are over). Then show us the anti-differentiated equation. You went wrong somewhere in there. Also, as Roshan has noticed, you don't quite seem to know how to manipulate logs.

These operations are valid: $log(a)+log(b)=log(a*b); \quad log(a)-log(b)= \displaystyle log\left(\frac{a}{b}\right)$.

Parentheses are VERY important when typing math online. You first statement when read at face value says $\displaystyle \int_1^2 \frac{x\ \ dx\ (x+2)}{x+1}$ which is obviously not what you meant.