Integration Problem

[perrrelet]

Can someone please integrate this for me?:

Integrate(sqrt(1+((4)(k^2)(x^-6))) dx

''Integrate: (The square root of (1 plus (4 times k squared times x to the minus 6)))''

Many Thanks

[Gnu]

Is this a question given as you've stated it, or is it the result of some other work that you've done?

What integration techniques are you using to solve other questions (parts, substitution etc.) and what maths topics are you working on at the moment (integrating trigonometric functions etc.)

This might help come up with the answer - it doesn't look obvious!

[jake-the-peg]

I assume you can handle the integration of the stuff inside the square root and it's the presence of the square root that's giving you trouble.

It's an example of integration by substitution.

have a look at example 2 on this page there's a Java or flash animation showing you how.

http://archives.math.utk.edu/visual.calculus/4/substitutions.3/index.html

In your example you've a 4Ksquared instead of a 7 and x is to the -6 but otherwise it's basically the same

[perrrelet]

Thankyou for your answer but it doesn't work in this situation.

With the e xample on that web page you can take the denominator of 'du' outside of the integral since it is a constant. However, in my problem the denominator of 'du' ends up as being ''(-24)(k^2)(x^-5)'' which is not a constant.

Any advice?

[perrrelet]

Message to: Gnu.

I have not been set this question it would be better to say that it has found me. I am working on a theory related to the curvature of space-time and i need to integrate this in order for me to find the lengths of some curves to see if what i believe could be true.

[jake-the-peg]

Have a look at example 6 then that looks closer

[Gnu]

I don't think that this integration is possible by 'standard' i.e. A level or even degree level techniques.

Do you have limits (plus or minus infinity would be OK) to allow a numerical integration?

I downloaded a computer algebra system on a trial basis (I think it was mulab) that wasn't able to integrate it, but it would allow you to perform the numerical integration to get an approximate answer.

[perrrelet]

The limits are 1 to 100.

Did you download the software? If so can i please have the link.

[Gnu]

The software is mupad (sorry!, not mulab) and the link is

http://www.mupad.de/download.html

It looks a bit daunting to start with, but the tutorial quickly goes through the basics.

Good luck!