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Math Help - Using change of variables to find indefinite integrals

  1. #1
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    Using change of variables to find indefinite integrals

    These problems are destroying my mind.

    \int 1/((10x-3)^2)

    So far I've... \int u^2 1/udu, u=10x-3

    After this is where my thoughts unravel.

    Maybe...

    (1/10) * (u^3)/3 = (1/10) * ((10x-3)^3)/3 ????


    The next one is

    \int (6x+1) * \sqrt{3x^2+x}dx where u is given and u = 3x^2+x

    I realize the derivative of 3x^2+x is 6x+1 and this offers some kind of portent but I fail to see the next logical step.

    Any help is appreciated.
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  2. #2
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    Quote Originally Posted by AlphaTauLambda View Post
    These problems are destroying my mind.

    \int 1/((10x-3)^2)

    So far I've... \int u^2 1/udu, u=10x-3

    After this is where my thoughts unravel.

    Maybe...

    (1/10) * (u^3)/3 = (1/10) * ((10x-3)^3)/3 ????


    The next one is

    \int (6x+1) * \sqrt{3x^2+x}dx where u is given and u = 3x^2+x

    I realize the derivative of 3x^2+x is 6x+1 and this offers some kind of portent but I fail to see the next logical step.

    Any help is appreciated.
    Rewrite the integral and then use substitution:

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  3. #3
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    I've worked out (with some help)
    u =10x-3
    du=10dx
    1/10du=dx

    1/10 * the integral of 1/u^2

    I've taken this to mean

    1/10 * -1/10x-3 or -1/100x-30

    where -1/100x-30 is the final solution.

    I'm having trouble deriving this, however. My answer comes out as 1/(100*x^2-60*x+9)
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  4. #4
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    Quote Originally Posted by AlphaTauLambda View Post
    I've worked out (with some help)
    u =10x-3
    du=10dx
    1/10du=dx

    1/10 * the integral of 1/u^2 Mr F says: Do this integral. Then substitute back u = 10x - 3.

    I've taken this to mean

    1/10 * -1/10x-3 or -1/100x-30 Mr F says: Yes, this is correct.

    where -1/100x-30 is the final solution.

    I'm having trouble deriving this, however. My answer comes out as 1/(100*x^2-60*x+9)
    ..
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  5. #5
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    Thank you, all. You have been wonderful. I'm much more suited for chemistry and biology... The worst math I have to worry about is michaelis mentin kinematics and mathemeticians such as yourselves have already mapped that bit all out.

    Thank you, again!
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