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



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

.Sam.
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Long division for the int. by parts?

appleduardo
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uhmm could that work?

anonymous
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my guess is parts

anonymous
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oh nvm you have that already

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

anonymous
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\[\frac{x^2}{x^2+1}=\frac{x^2+1}{x^2+1}\frac{1}{x^2+1}=1\frac{1}{x^2+1}\]

anonymous
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first integral is obvious, second part is the derivative of arctangent

anonymous
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i ignored the 2, @.Sam. has it

anonymous
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you could divide too, but i find that gimmick easier than long division

appleduardo
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thank you! I'll try and post it when im done :P