Question

Rewrite \(\int^3_2\frac{3x}{x^2-4x+5}\,dx\) into the form of \(\int^b_a\frac{mt+c}{t^2+k^2}\) or \(\int^b_a\frac{mt+c}{t^2-k^2}\).

Completing the square, as far as I can see, wouldn't work this time. What should I do with this?

Answer 1

It works :)

Answer 2

\[\int^3_2\frac{3x}{x^2-4x+5}dx=\int^3_2\frac{3x}{x^2-4x+(4+1)}dx=\int^3_2\frac{3x}{(x-2)^2+1}dx\]In this case, t=x-2, k=1

Answer 3

*facepalm*
I am such an idiot.

Answer 4

No, you're not..