# Solve $\int{\sqrt{1 + (3x^2 + 2x - \frac{29}{2})^2}} dx$

I have to solve this indefine integral:

$$\int{\sqrt{1 + (3x^2 + 2x - \frac{29}{2})^2}} dx$$

I tried to make the square:

$$\int{\sqrt{9x^4 +12x^3-29*3x^2 -58x + \frac{29^2 +4}{4}}} dx$$

but this makes me confused more than first. I don't know how to do substitution for this case or any other method. I have no idea. Can you please help me?

Thank you!

• Please tell me if you don't understand something I write. I'm not very good at english. Thank you! – MM PP Jul 15 '16 at 5:51
• This is a nice monster which can be solved using elliptic integrals. However, looking at your next post, you do not need this one. – Claude Leibovici Jul 15 '16 at 6:51
• @ClaudeLeibovici the next post is not related to this one. It is a coincidence the integral is the same :) first exercise is this, then next exercise is my latest post – MM PP Jul 15 '16 at 6:52