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anonymous

  • 5 years ago

Evaluate the integral question inside!

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  1. anonymous
    • 5 years ago
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    \[\frac{x^{2} dx }{x^3-e^3}\]

  2. amistre64
    • 5 years ago
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    e^3 is a constant

  3. anonymous
    • 5 years ago
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    Clue: u is usually thingy on the bottom u would have a du on top

  4. anonymous
    • 5 years ago
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    Here is my answer: \frac{1}{3} ln (x^{3} - e^{3}) + C

  5. amistre64
    • 5 years ago
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    u = x^3 - e^3 ; du = 3x^2 dx ; dx = du/3x^2

  6. anonymous
    • 5 years ago
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    eek!

  7. amistre64
    • 5 years ago
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    x^2 du ------- 3x^2 u du ----- = (1/3) ln(u) +C 3 u

  8. amistre64
    • 5 years ago
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    i wonder: (x^3-e^3) is a difference of cubes; can we split it to simplify further?

  9. amistre64
    • 5 years ago
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    (x-e)(x^2 +x e +e^2) :)

  10. anonymous
    • 5 years ago
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    yay! that's the answer I have! \[\frac{1}{3} \ln (x^{3} - e^{3} ) + C\]

  11. amistre64
    • 5 years ago
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    leave it :)

  12. anonymous
    • 5 years ago
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    hmph! Not the final answer?

  13. anonymous
    • 5 years ago
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    lol!

  14. anonymous
    • 5 years ago
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    Thank you so much for the confirmation!

  15. amistre64
    • 5 years ago
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    should we put the 1/3 as an exponent inside the ln?

  16. amistre64
    • 5 years ago
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    i dont see much more we can do to simplify it :)

  17. anonymous
    • 5 years ago
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    Me either! Phew, you had me worried! lol

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