Question

complete the square and integrate:
integral (x / (x^2+4x+6)^(1/2))

Answer 1

\[\int\limits \frac{x}{\sqrt{x^2 + 4x + 6}}dx=\int\limits \frac{x}{\sqrt{x^2 + 4x + 4 + 2}}dx\]\[= \int\limits \frac{x}{\sqrt{(x + 2)^2 + 2}}dx\]\[u = x + 2\]\[du = dx\]\[x = u - 2\]\[= \int\limits \frac{u - 2}{\sqrt{u^2+2}}du\]continue with trig substitution

Answer 2

thanks!

Answer 3

A suggestion
\[ u= \sqrt 2\tan (v)
\]