Integral Problem

[Coletrane315]

I found this problem on a facebook meme. I just graduated high school and took AP Calculus, I do a lot of independent research, but by no means would I say I'm professional with it. I attempted integration by parts. After one iteration, it became so complex it would minimum involve a triple product rule derivative, so many terms. Theoretically, at least in my thought, it would continuously give me another integral by parts to do. Any advice would help a lot. Note: I also attempted to make a general formula for a quotient rule for integrals, had the same issue.

[MATH]\int_{0}^{1} \frac{3x^3-x^2+2x-4}{\sqrt{x^2-3x+2} } dx [/MATH]

 

[topsquark]

Integration by parts would be a mess. Rule of thumb: When in doubt and you have a quadratic in the denominator, try completing the square. It's not an easy solution (I don't think that there's any easy method for this one) but if you complete the square under the radical and use the substitution u = x - 3/2 and follow it up with [math] u = \dfrac{1}{2} sec( \theta )[/math] it can be done. (There's a lot of Trig involved.)

-Dan

 

[Steven G]

x=1 is a root for the numerator and denominator. I would factor and would suspect that should make the integrand simpler looking.