ethayer
integral of (3t2)/(t+1)



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TuringTest
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easiest way is probably\[u=t+1\implies t=u1\]\[du=dt\]

TuringTest
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long division would also work

CliffSedge
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I tried it with long division and it was pretty easy that way.

anonymous
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i like the gimmick of writing
\[3t2=3t+35\]

ethayer
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where do I go with long division after I get 3 remainder 5?

anonymous
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so you get
\[\frac{3t2}{t+1}=\frac{3t+35}{t+1}=1\frac{5}{t1}\]

anonymous
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oops
\[\frac{3t2}{t+1}=\frac{3t+35}{t+1}=3\frac{5}{t1}\]

anonymous
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then integrate each piece
first one gives you \(3x\) second gives you \(5\ln(t1)\)

ethayer
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ah got it thanks very much

anonymous
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damn another typo!!
should be
\[3x5\ln(x+1)\]

RaphaelFilgueiras
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