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henpen

  • 3 years ago

\[ \int \frac{x}{x^2+1}dx \]

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  1. phi
    • 3 years ago
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    this (almost) looks like u^-1 du

  2. henpen
    • 3 years ago
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    This smells of parts, but I'm having trouble with \[\int\limits \frac{1}{x^2+1}dx\]

  3. sirm3d
    • 3 years ago
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    that is arctangent

  4. henpen
    • 3 years ago
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    Although that might not help

  5. sirm3d
    • 3 years ago
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    can you enlighten us with the problem?

  6. klimenkov
    • 3 years ago
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    Do a substitution \(u=x^2, du=2xdx\)

  7. henpen
    • 3 years ago
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    \[0.5 \ln(u+1)\]

  8. henpen
    • 3 years ago
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    @sirm3d It's halfway through the DE of my last question

  9. klimenkov
    • 3 years ago
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    Yes. Now make the inverse substitution.

  10. sirm3d
    • 3 years ago
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    post a link @henpen

  11. henpen
    • 3 years ago
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    http://openstudy.com/users/henpen#/updates/50968019e4b0d0275a3ce47b

  12. sirm3d
    • 3 years ago
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    hmm, can we try reduction of order with \[y=v(ix)\]

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