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Math Help - integrating help

  1. #1
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    integrating help

    \int\limits_0^1\frac{dx}{(1+x)\sqrt{8x^2+14x+5}}

    with substitution
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by stud_02 View Post
    \int\limits_0^1\frac{dx}{(1+x)\sqrt{8x^2+14x+5}}

    with substitution
    Try rewriting the square root in the denominator with (x+1).

    8x^2+14x+5 = 8(x+1)^2-2(x+1)-1

    Then use u=x+1 and du=dx

    Now you have \int_0^1\frac{1}{u\sqrt{8u^2-2u-1}}\,du

    This should make it a little easier, though to be honest I'm not sure where to go from here. I'll edit in additional steps if I think of them.

    If you want it, the final answer (according to Maple) is:
    Spoiler:
    \int\frac{1}{(1+x)\sqrt{8x^2+14x+5}}\,dx = \arctan\left(\frac{-x-2}{\sqrt{8x^2+14x+5}}\right)
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  3. #3
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    Sub sqrt(8x^2 + 14x + 5) + x = u , It is known as Euler's Substitution
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  4. #4
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    starting from redsox's...









    that should help you.
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