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anonymous

  • 5 years ago

Evaluate: anti-derivative x dx/sqrt(x^2+1)

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  1. anonymous
    • 5 years ago
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    I get u= x^2+1 du = 1 dx

  2. anonymous
    • 5 years ago
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    put x^2 +1 =t diff w.r.t. x , we get 2x dx= dt

  3. anonymous
    • 5 years ago
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    i.e. x dx= dt/2

  4. anonymous
    • 5 years ago
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    u could even substitute sqrt(x^2+1)=t than can work too

  5. amistre64
    • 5 years ago
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    tan(t) = x ; dt sec^2 = dx; t = tan^-1(x)..lets start :) x dx tan(t) sec^2(t) dt -------- --> --------------- (x^2 +1) tan^2 +1 <-- this is eqaul to sec^2

  6. amistre64
    • 5 years ago
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    [S] tan(t) dt

  7. anonymous
    • 5 years ago
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    (x^2 + 1)^1/2 + c

  8. amistre64
    • 5 years ago
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    yeah, it helps if you read the sqrt part ;).....

  9. amistre64
    • 5 years ago
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    ...if you ever need to do the one I was working on....lol

  10. amistre64
    • 5 years ago
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    when I re did it with the approriate sqrt.... I got\[\int\limits_{}\frac{\tan(t)\sec^2(t)}{\sec(t)}dt \rightarrow \int\limits_{} \sec(t)\tan(t)dt \rightarrow \sec(t)\]

  11. amistre64
    • 5 years ago
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    \[\sec(t) = \sqrt{x^2+1}\]

  12. amistre64
    • 5 years ago
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    +C lol

  13. anonymous
    • 5 years ago
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    I started a new problem

  14. amistre64
    • 5 years ago
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    yay!! .... I was just trying to wrap this one up in me brain :)

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