Integration by trig. substitution

[mad]

Hello everyone
I have an exam tomorrow and I would really appreciate if someone could tell me what I did wrong with this exercice. I did it on paper and I scanned it. Here is the link to the scan:

The answer in the book is sqrt(x^2 + x +5/4) + 2ln(sqrt(x^2 + 2x + 2) + x +1) + C

http://img223.echo.cx/img223/8425/problem490012al.jpg

It is hosted on imageshack.us
download it and open it in windows so you can change the zoom size for better viewing

Thanks a lot in advance !

 

[theCandyman]

If u = x + 1, where does u + 1 come from? That is just the first thing I saw, it may lead to your other problems.

 

[dextercioby]

It should be "u+2" in the numerator after doing the first sub.

Daniel.

 

[mad]

It should be "u+2" in the numerator after doing the first sub.

Daniel.

Woops. Was this the only problem? I think this only changes the arctg from the final answer and not the ln(..) of the answer. I hate when this type of error happens..

 

[whozum]

When translating from theta back to x, you mistranslated sec(t).

Next to the triangle you have

$$sec(\theta) = \frac{1}{\cos(\theta)} = \frac{1}{u}$$

cos(theta) is not u, try looking at it again.

 

[mad]

When translating from theta back to x, you mistranslated sec(t).

Next to the triangle you have

$$sec(\theta) = \frac{1}{\cos(\theta)} = \frac{1}{u}$$

cos(theta) is not u, try looking at it again.

Thanks a lot :)