Hello, please assist with the following:

Find An Antiderivative of the following:

1.) X/(X+1)

2.) 1/(X+1)^2

Please show working, thanks!

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- Aug 14th 2009, 02:17 AMandrew2322Antidifferentiation Help
Hello, please assist with the following:

Find An Antiderivative of the following:

1.) X/(X+1)

2.) 1/(X+1)^2

Please show working, thanks! - Aug 14th 2009, 02:41 AMenjam
Ok, for the first one:

x / (x + 1) = 1 - (1 / (x+1))

∫ 1 dx - ∫ (1 / (x+1) dx

= x - log (x+1) + C

For the second one:

∫ (x+1)^-2 . dx

= (-1)(x+1)^(-2+1)

= -1/(x+1) + C - Aug 14th 2009, 05:07 AMmr fantastic
- Aug 14th 2009, 07:20 AMsongoku
Hi enjam and mr fantastic

A little correction : "log" should be "ln" :) - Aug 14th 2009, 07:53 PMandrew2322Thanks
Thanks for the assistance but could you please explain how you got 1 - (1/(x+1))?

- Aug 14th 2009, 08:03 PMsongoku
Hi andrew2322

Use long division to divide x by (x+1) - Aug 14th 2009, 08:26 PMmr fantastic