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Math Help - calculus 2/integrals

  1. #1
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    calculus 2/integrals

    Hi everyone,

    Can you please tell me if this is correct and if it isn't can you give me a hint or explain to me why it is wrong?

    Evaluate the following integrals:

    X/(X^2+1)^2dx

    u=x^2+1
    du+2xdx
    xdx=du/2

    x/(x^2+1)^2dx=
    1/u^2du/2=
    1/lnu^2+c=
    1/2ln(x^2+1)^2

    Thank you very much

    P.S.
    Does anyone know how to add math symbols on the computor? that is, how to add a square root, x squared etc.
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by chocolatelover View Post
    Hi everyone,

    Can you please tell me if this is correct and if it isn't can you give me a hint or explain to me why it is wrong?

    Evaluate the following integrals:

    X/(X^2+1)^2dx

    u=x^2+1
    du+2xdx
    xdx=du/2

    x/(x^2+1)^2dx=
    1/u^2du/2=
    1/lnu^2+c= <==== here you made your mistake
    1/2ln(x^2+1)^2

    ...
    Hello,

    remember \int \frac{1}{x^2}dx = -\frac{1}{x} +C
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by chocolatelover View Post
    Hi everyone,

    Can you please tell me if this is correct and if it isn't can you give me a hint or explain to me why it is wrong?

    Evaluate the following integrals:

    X/(X^2+1)^2dx

    u=x^2+1
    du+2xdx
    xdx=du/2

    x/(x^2+1)^2dx=
    1/u^2du/2=
    1/lnu^2+c=
    1/2ln(x^2+1)^2

    Thank you very much
    You started off nicely, then it went horribly wrong ... well, not horribly, i'm exagerated, i can see how you made that mistake

    doing what you did:

    \int \frac {x}{\left( x^2 + 1 \right)^2}~dx

    We proceed by substitution:

    Let u = x^2 + 1

    \Rightarrow du = 2x~dx

    \Rightarrow \frac {1}{2}du = x~dx

    So our integral becomes:

    \frac {1}{2} \int \frac {1}{u^2}~du

    THIS IS WHERE YOU MADE THE MISTAKE, THIS INTEGRAL DOES NOT GIVE \color {red} \ln (u)

    \frac {1}{2} \int \frac {1}{u^2}~du = \frac {1}{2} \int u^{-2}~du .........now use the power rule

    = - \frac {1}{2}u^{-1} + C

    = - \frac {1}{2 \left( x^2 + 1 \right)} + C


    P.S.
    Does anyone know how to add math symbols on the computor? that is, how to add a square root, x squared etc.
    do you know how to use LaTex? see the LaTex Tutorial on this site

    otherwise, to say "the square root of x" you would type "sqrt(x)"
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  4. #4
    Member
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    Thank you very much

    Regards
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