# Integration by parts [Solved!]

**phinah** 06 May 2020, 14:52

### My question

Write the following fraction as a sum of partial fractions and then integrate with respect to x. It's Exercise 1 on the linked page.

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

โ

### Relevant page

11. Integration by Partial Fractions

### What I've done so far

We solved it exactly as you did. However, we differ when it comes to the final line.

We have as the solution's second term: `-1/2 ln (x^2).`

Please show us how you arrived at the second term in your solution.

Thank you.

X

Write the following fraction as a sum of partial fractions and then integrate with respect to x. It's Exercise 1 on the linked page.
`1/(x^2(x-2))`
โ

Relevant page
<a href="/methods-integration/11-integration-partial-fractions.php">11. Integration by Partial Fractions</a>
What I've done so far
We solved it exactly as you did. However, we differ when it comes to the final line.
We have as the solution's second term: `-1/2 ln (x^2).`
Please show us how you arrived at the second term in your solution.
Thank you.

## Re: Integration by parts

**Murray** 07 May 2020, 03:19

The second term that needs integrating is

`int -1/(2x^2) dx`

This is equivalent to

`int -1/2 x^(-2) dx = -1/2(x^(-2+1)/(-2+1)) ` `= -1/2((x^-1)/(-1))` `=(1/2)(1/x) = 1/(2x)`

X

The second term that needs integrating is
`int -1/(2x^2) dx`
This is equivalent to
`int -1/2 x^(-2) dx = -1/2(x^(-2+1)/(-2+1)) ` `= -1/2((x^-1)/(-1))` `=(1/2)(1/x) = 1/(2x)`

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