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anonymous

  • 5 years ago

Use U-Substitution to evaluate the Integral:

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  1. anonymous
    • 5 years ago
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    u=(x^{4} + 3x^{2} +5)

  2. anonymous
    • 5 years ago
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    \[\int\limits_{?}^{?} (4x^{3} +6x) \cos (x^{4} + 3x^{2} + 5 ) dx\]

  3. anonymous
    • 5 years ago
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    I have to integrate that above this post with the U given in the first post. Please confirm my answer if you can!!

  4. anonymous
    • 5 years ago
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    Actually I couldn't get an answer - please helpz!!!

  5. anonymous
    • 5 years ago
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    = sin ( u ) = sin ( x^4 + 3x^3 + 5) + C

  6. anonymous
    • 5 years ago
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    sorry the second x should be squared ( 3x^2)

  7. anonymous
    • 5 years ago
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    because u = x^4 + 3x^3 + 5 ==> du/dx = 4x^3 + 6x solve for dx and plug the equation for dx into the integral

  8. anonymous
    • 5 years ago
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    if you write that out you will notice you have 4x^3 + 6x in the numerator and denominator and that equals 1. but you are still multiplying by du. because you had to solve for dx

  9. anonymous
    • 5 years ago
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    you get \[\int\limits_{?}^{?}\cos u du\] = sin u then just plug u back into the sing

  10. anonymous
    • 5 years ago
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    taking a step back when you solve for dx you should get dx = du / (4x^3 + 6x) plug that into the integral. you are integrating du with respect to u

  11. anonymous
    • 5 years ago
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    \[\sin(x^{4} + 3x^{2} + 5) + c \]

  12. anonymous
    • 5 years ago
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    perfect

  13. anonymous
    • 5 years ago
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    awesome!! thank you so much!!

  14. anonymous
    • 5 years ago
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    yeahp!

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