# Antidifferentiation Help

• Aug 14th 2009, 02:17 AM
andrew2322
Antidifferentiation Help
Hello, please assist with the following:

Find An Antiderivative of the following:

1.) X/(X+1)

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

• Aug 14th 2009, 02:41 AM
enjam
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 AM
mr fantastic
Quote:

Originally Posted by enjam
Ok, for the first one:

x / (x + 1) = 1 - (1 / (x+1))
∫ 1 dx - ∫ (1 / (x+1) dx
= x - log |x+1| + C
[snip]

Correction in red.
• Aug 14th 2009, 07:20 AM
songoku
Hi enjam and mr fantastic

A little correction : "log" should be "ln" :)
• Aug 14th 2009, 07:53 PM
andrew2322
Thanks
Thanks for the assistance but could you please explain how you got 1 - (1/(x+1))?
• Aug 14th 2009, 08:03 PM
songoku
Hi andrew2322

Use long division to divide x by (x+1)
• Aug 14th 2009, 08:26 PM
mr fantastic
Quote:

Originally Posted by songoku
Hi andrew2322

Use long division to divide x by (x+1)

Alternatively .... $\displaystyle \frac{x}{x + 1} = \frac{(x + 1) - 1}{x + 1} = \frac{x + 1}{x + 1} - \frac{1}{x + 1} = 1 - \frac{1}{x + 1}$.