1. ## Antidifferentiation Help

Hello, please assist with the following:

Find An Antiderivative of the following:

1.) X/(X+1)

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

2. 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

3. 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.

4. Hi enjam and mr fantastic

A little correction : "log" should be "ln"

5. ## Thanks

Thanks for the assistance but could you please explain how you got 1 - (1/(x+1))?

6. Hi andrew2322

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

7. Originally Posted by songoku
Hi andrew2322

Use long division to divide x by (x+1)
Alternatively .... $\frac{x}{x + 1} = \frac{(x + 1) - 1}{x + 1} = \frac{x + 1}{x + 1} - \frac{1}{x + 1} = 1 - \frac{1}{x + 1}$.