How to evaluate $\int_0^1\frac{3x^3-x^2+2x-4}{\sqrt{x^2-3x+2}}~dx$?

Question

What is the best method with which to approach the following integral?

$$\int_0^1 \frac{3x^3-x^2+2x-4}{\sqrt{x^2-3x+2}}dx$$

Thanks

Welcome to MathSE. Instead of adding a photo, please use MathJax! — , Nov 03 '18 at 17:23
Welcome to MSE. Questions like "Here is the task. Solve it for me!" are poorly received on this site. Therefore try to improve your question with an edit. Improving could consist of providing some context concerning your task or by adding what you have tried so far and where did you struggle :) — mrtaurho, Nov 03 '18 at 17:25
See also: Problem about evaluating $\int_0^1 {3x^3 -x^2 +2x -4\over \sqrt {x^2-3x+2} } ; dx$, How do you evaluate $\int_{0}^{1} \frac{(3x^3-x^2+2x-4)}{\sqrt{x^2-3x+2}}$?, How to integrate the product ... and other questions linked there — Martin Sleziak, Dec 13 '19 at 15:29

score 2 · Answer 1 · answered Nov 03 '18 at 17:33

2

Hint: Use the substitution $$\sqrt{ax^2+bx+c}=\pm x\sqrt{a}+t$$ It is the so-called Euler Substitution.

answered Nov 03 '18 at 17:33

1 Answers1