Question

Find the indefinite integral of:

x-4
---------
(x^2 + 2)^2

dx

Answer 1

I would like a hint please, not the answer.

Answer 2

take x^2+2 = t That's the hint

Answer 3

partial fractions is the only hint I can think of
...^that sub wasn't working for me, but maybe I messed up

Answer 4

also a trig sub could work

Answer 5

...but that would be ugly

Answer 6

And write it separately like
\[\int\limits_{}^{} ({{x}\over ({x^2+2})^2} - {{4} \over (x^2+2)^2}) dx\]

Answer 7

Shivam I tried that but how would you do it for the latter term? I realized that I could just use Trig sub and it would work out fine. I get secx's cancelling from the denominator.

Answer 8

@TuringTest , a trig substitution of x = sqrt(2) tan (theta) can also help

Answer 9

@QRAwarrior , yes it would get ugly that way. trig substitution seems the best way out

Answer 10

@QRAwarrior , I confirm I am getting the answer with trig substitution of x = sqrt(2) tan (theta) easily.