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anonymous

  • 5 years ago

compute the indefinite integral: dx/(x^2+4)^(5/2)

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  1. anonymous
    • 5 years ago
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    If I'm not mistaken, you can use trigonometric substitution : you have the following: \[\int\limits_{}^{}1/\sqrt{(x^2 + 4)^5}dx\] we have the form : \[\sqrt{x^2 + a^2}\] so you can let x be: \[x = a \tan \theta\] Then substitute x in : \[\sqrt{(x^2 + 4)^5}\] After that find dx when x = atan(theta) Last , susbstitute everything in the integral and then integrate. Give it a try now ^_^

  2. anonymous
    • 5 years ago
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    thank you so much!

  3. anonymous
    • 5 years ago
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    i also have another question...the original question is: compute the integral: ∫01(8x2+6)/(x2+1)(x+7)dx

  4. anonymous
    • 5 years ago
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    ∫(8x2+6)/(x2+1)(x+7)dx

  5. anonymous
    • 5 years ago
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    np :)

  6. anonymous
    • 5 years ago
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    use partial fractions for this one so you'll have the following form:\[= (A/x^2 + 1) + (B/x+7)\] try it out ^_^

  7. anonymous
    • 5 years ago
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    and after that you plug in the value right?

  8. anonymous
    • 5 years ago
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    you'll have to multiply by the denominators to get the following state: \[8x^2 +6 = A(x+7) + B(x^2+1)\] then try out small numbers for x, then plug it in ^_^

  9. anonymous
    • 5 years ago
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    example, take x = 0 then x = 1 :)

  10. anonymous
    • 5 years ago
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    to get values for A and B, then find the integral :)

  11. anonymous
    • 5 years ago
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    thanks you are a BIG HELP!

  12. anonymous
    • 5 years ago
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    you're welcome, glad I could help ^_^

  13. anonymous
    • 5 years ago
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    \[\int\limits_{0}^{1} \ln(x) / x ^{1/2} dx \] to approximate this integral using the trapezoid rule. if you can help me with this one also, i am sorry :(

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