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IntMath forum | Methods of Integration

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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