# Indefinite Integration

• May 2nd 2012, 12:48 PM
Ivanator27
Indefinite Integration
I've got another integral that I can't solve. =/ I know it looks really ugly but I'm certain it's correct.

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

If I've missed something really obvious I'd appreciate it if you gave me a hint and not the full solution. Thanks in advance.
• May 3rd 2012, 06:36 AM
HallsofIvy
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.
• May 3rd 2012, 09:53 AM
Ivanator27
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?
• May 3rd 2012, 02:06 PM
TheIntegrator
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
• May 3rd 2012, 02:17 PM
Ivanator27
Re: Indefinite Integration
k and u are both constants, and yes - the aim is to integrate in terms of x.