Mastering Indefinite Integrals: Tips and Tricks for Evaluating Tricky Functions

[uman]

How can I evaluate $\int\frac{dx}{\sqrt{1-2x-x^2}}$ using inverse trig functions? Thanks.

 

[rock.freak667]

complete the square of the quadratic.

 

[uman]

Oh... thanks.

Dang these are so hard... I wish I had the creativity to see the solution immediately like that...

 

[rocomath]

ax^2+bx+c, a=1, factor out the negative before you complete the square if you didn't remember.

 

[uman]

Thanks. I got the right answer after rock.freak667's hint. I just wish I were able to solve these more easily, without hints from this forum and elsewhere... does it just take lots of practice, or what?

 

[rocomath]

Read read read! And do the practice problems :-]

Go here to see a variety of diff. methods.

http://www.mathlinks.ro/weblog_entry.php?p=992552#992552
http://www.mathlinks.ro/weblog_entry.php?p=992575#992575
http://www.mathlinks.ro/weblog_entry.php?p=992703#992703

 

[Gib Z]

When it comes to integrals, its experience that really counts. Do as many integrals as you can, you'll soon learn the tricks of the trade.