More integration

[qwertysaur]

I have a very annoying problem that I can't get. =/

∫ (X + 1)/(x² + 4x + 8) dx

[Aerith's Knight]

I just filled two pages with partial integrals, imaginary numbers, splitting equations and a whole bunch of other crap. Then I decided to look at the answer, which came to

-0.5 * ArcTan[(2+x)/2] + 0.5*Log[x^2 +4x +8]

Which will be annoyingly complicated. So could you check first if the question itself wasn't wrong?

I can get you started by:

∫ (X + 1)/(x2 + 4x + 8) dx = ∫ X/(x2 + 4x + 8) dx + ∫ 1/(x2 + 4x + 8) dx

Where ∫ 1/(x2 + 4x + 8) dx = ln(x2 + 4x + 8)/(2x + 4) + C

Also, x2 + 4x + 8 = (x - 2 - 2j)(x - 2 + 2j), but I doubt that helps.

[qwertysaur]

I feel bad that you had two pages of work to do, but I really appreciate it. I took the derivative of your answer, and now I get it. Thanks :)

[SeeDRankLou]

Is the "X" a typo for "x", or is the "X" different than the "x"?

[rubah]

Sepho felt that he must share his solution with you all
http://rubah.net/sepho/solution.png

[Jessweeee♪]

The day is saved!