what are some integration techniques to approach a quadratic in a radical where b =/= 0?

[Al-Layth]

i see this structure appear in various integrals:
[math]\sqrt{ax^2 +bx +c}[/math]
what are some approaches to deal with this form aside from completing the square and substituting ax+b, and aside from euler substitutions??

 

[blamocur]

I would reduce it to [imath]\sqrt{u^2\pm 1}[/imath], then use substitutions with trigonometric functions.

 

[Steven G]

I would reduce it to [imath]\sqrt{u^2\pm v^2}[/imath], then use substitutions with trigonometric functions.

 

[Al-Layth]

I would reduce it to [imath]\sqrt{u^2\pm v^2}[/imath], then use substitutions with trigonometric functions.

So how would you reduce it to that ?

 

[pka]

So how would you reduce it to that ?

SEE HERE

 

[Steven G]

So how would you reduce it to that ?

Complete the square