- #1

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## Homework Statement

[tex]\int \frac {x}{x+ \sqrt {x+2}}[/tex]

## The Attempt at a Solution

I used the v-sub.

I also did a long division.

It gave me [tex]\int 2v-2- \frac {v}{v-1} + \frac {2}{v-1}[/tex]

My final answer [tex]2x+2-2 \sqrt {x+2} -ln \sqrt {x+2} -1 +2ln \sqrt {x+2} -1 +c[/tex]

The final answer should be [tex]x-2 \sqrt {x+2} - 2/3ln \sqrt {x+2} -1 + \frac 8/3ln \sqrt {x+2} + 2 +c[/tex]

Where is my mistake?