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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