# Integration by parts [Solved!]

### 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))

### 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))
​
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

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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