Re: Indefinite Integration

No, there is nothing "really obvious". That is, as you say, an ugly integral and it cannot be done in any simple way.

Re: Indefinite Integration

Trigonometric substitution seems out the window because of the ln|x| in the denominator.

Doing it by parts doesn't seem to work.

http://latex.codecogs.com/gif.latex?...ku}x^{4}+k}}dx

http://latex.codecogs.com/gif.latex?...20\right%20]dx

Now looking only at this part of the second term...

http://latex.codecogs.com/gif.latex?...}%20\right%20)

http://latex.codecogs.com/gif.latex?...}%20\right%20]

http://latex.codecogs.com/gif.latex?...)%20\right%20)

etc. So the second integral doesn't look like it can be simplified into anything workable.

So the solution must concern normal u-substitution or some method of integration that I'm not familiar with. I was looking for another method of integration and I read about something called 'Integration by Using Parametric Differentiation', I didn't really understand the article so perhaps that's necessary here?

Re: Indefinite Integration

I assume we are integrating with respect to x - What are k and u? Not the actual values, but are they supposed to be differentiable functions of a variable, or constants, or . . . You need this information to integrate

Re: Indefinite Integration

k and u are both constants, and yes - the aim is to integrate in terms of x.