# Integral trig substitution

1. May 12, 2010

### apiwowar

integral of x/(x2+2x+2)dx

first thing i did was complete the square to get

x/((x+1)2+1

i tried then having x+1 = tanx but that didnt work out

because of the x on top i cant just set w = x+1

what would the right substitution be?

any hints or help would be appreciated

2. May 12, 2010

### TheoMcCloskey

apiwowar - try one more substitution, u = (x+1). This will yield two terms in numerator, thus two fractions, for which you should be able to integrate separately with a little more manipulation.

3. May 13, 2010

### Cyosis

Using the substitution $x+1=\tan u$ will work just fine. However the substitution in post #2 will make it easier. Show us where you got stuck.

4. May 13, 2010

### apiwowar

i did the substitution that the first guy suggested and got 1/2ln((x+1)2+1) - arctan(x+1)

is that right?

5. May 13, 2010

### TheoMcCloskey

That is what I obtained (don't forget constant of integration).

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