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Partial Fraction [Solved!]

My question

In example 4, the numerator in the next-to-last step is `(1/2)x + 1.`

How did you go from that to the numerator 'x+2' in the final step?

Relevant page

11. Integration By Partial Fractions

What I've done so far

Stuck at the next-to-last step. Do not know how to handle the 'x' in the numerator.

X

In example 4, the numerator in the next-to-last step is `(1/2)x + 1.`

How did you go from that to the numerator 'x+2' in the final step?
Relevant page

<a href="https://www.intmath.com/methods-integration/11-integration-partial-fractions.php">11. Integration By Partial Fractions</a>

What I've done so far

Stuck at the next-to-last step.  Do not know how to handle the 'x' in the numerator.

Re: Partial Fraction

@Phinah: If I multiply a number by `2/2`, does the value of that number change...?

X

@Phinah: If I multiply a number by `2/2`, does the value of that number change...?

Re: Partial Fraction

No because you are multiplying it by 1

X

No because you are  multiplying it by 1

Re: Partial Fraction

You are multiplying the number by 1

X

You are multiplying the number by 1

Re: Partial Fraction

So I gather you can see how

`(1/2x+1)/(x^2+1)`

becomes

`(x+2)/(2(x^2+1))`

now?

X

So I gather you can see how

`(1/2x+1)/(x^2+1)`

becomes

`(x+2)/(2(x^2+1))`

now?

Re: Partial Fraction

Yes! Thanks.

X

Yes! Thanks.

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