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appleduardo

  • 2 years ago

whats the integral of ln(x^(2) + 1)??

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  1. appleduardo
    • 2 years ago
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    so far I have:\[\ln(x ^{2}+1)x-\int\limits_{}^{}x*\frac{ 2x }{ x ^{2}+1 } dx\]

  2. .Sam.
    • 2 years ago
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    Long division for the int. by parts?

  3. appleduardo
    • 2 years ago
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    uhmm could that work?

  4. satellite73
    • 2 years ago
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    my guess is parts

  5. satellite73
    • 2 years ago
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    oh nvm you have that already

  6. .Sam.
    • 2 years ago
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    \[\ln(x ^{2}+1)x-\int\limits\limits_{}^{}2-\frac{2}{x^2+1} dx \]

  7. satellite73
    • 2 years ago
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    \[\frac{x^2}{x^2+1}=\frac{x^2+1}{x^2+1}-\frac{1}{x^2+1}=1-\frac{1}{x^2+1}\]

  8. satellite73
    • 2 years ago
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    first integral is obvious, second part is the derivative of arctangent

  9. satellite73
    • 2 years ago
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    i ignored the 2, @.Sam. has it

  10. satellite73
    • 2 years ago
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    you could divide too, but i find that gimmick easier than long division

  11. appleduardo
    • 2 years ago
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    thank you! I'll try and post it when im done :P

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