How Do You Integrate 1/(x^2+80x+1600)?

[Daniel Tyler]

Hi,

I'm v rusty on my integration so was wondering could anyone give me some guidance on how to find the solution to the following integral

integral (1/x^2+80x+1600)dx between the limits x=80 and x=0

Any help is much appreciated!

Regards

Daniel

 

[Daniel Tyler]

to be clearer its 1/(x^2+80x+1600)dx!

 

[berkeman]

Hi,

I'm v rusty on my integration so was wondering could anyone give me some guidance on how to find the solution to the following integral

integral (1/x^2+80x+1600)dx between the limits x=80 and x=0

Any help is much appreciated!

Regards

Daniel

to be clearer its 1/(x^2+80x+1600)dx!

I's start by factoring the denominator. What is the context of the question? Where did this integral come up?

 

[Svein]

to be clearer its 1/(x^2+80x+1600)dx!

To me, it looks like \frac{1}{(x+40)^{2}}. So, if you set u=(x+40), you get du=dx and x=u-40. This leaves you with an eminently solvable integral.