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

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

    Quote Originally Posted by Roger44 View Post
    Hi
    Can anybody help me with this one : integral of dx/(a^2 + bx + x^2)^1.5
    Have a look HERE.
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    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.
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    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.
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  5. #5
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    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?
    Thanks again in advance

    integral of dx/(a^2 + bx + x^2)^1.5-forum-sq-1.jpg
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  6. #6
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    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.
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