# Thread: integral of dx/(a^2 + bx + x^2)^1.5

1. ## integral of dx/(a^2 + bx + x^2)^1.5

Hi
Can anybody help me with this one : integral of dx/(a^2 + bx + x^2)^1.5

Thanks

2. ## Re: integral of dx/(a^2 + bx + x^2)^1.5

Originally Posted by Roger44
Hi
Can anybody help me with this one : integral of dx/(a^2 + bx + x^2)^1.5
Have a look HERE.

3. ## Re: integral of dx/(a^2 + bx + x^2)^1.5

You would complete the square in the polynomial and then look for a trigonometric substitution, I think.

4. ## Re: integral of dx/(a^2 + bx + x^2)^1.5

Plato, the link you gave me was perfect. Two other sites I had tried before didn't find a solution. Many thanks

The formula I submitted gives the lumens/sq m on a point on the floor coming from a bulb fixed to the wall, and this integral will give me lumens/sq m on a point on the floor coming from a horizontal strip of light fixed to the wall.

5. ## Re: integral of dx/(a^2 + bx + x^2)^1.5

Hello again

Wolfram gives this solution for another integral but as you can see only if a>b. Or this is a real world situation where a will be rarely less than b. Any workaround?

6. ## Re: integral of dx/(a^2 + bx + x^2)^1.5

Hi
I've just discovered the world of improper discontinous integrals, a level I didn't need to reach at school. I'm old now but it's never too late.

I see this sort of example quoted : integral from 0 to 3 of 1/(9-x^2) dx which can be solved by limits.
But what do you do with : integral from 0 to 4 (four) of the same function? I can break it up into 0 to 3 which is solvable by limits, but what do I do with the part >3? I can't just ignore it. Any help or any useful link would be welcome.

By the way, an approximate integral of dx/(a^2 + bx + x^2)^1.5 can be found with an Excel spreadsheet table which gives perfectly coherent values when b^2>a^2 so I'm a bit perplexed.