matchup | Integral ln(x)

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matchuplab	0.2	0.7	4645	37
matchups nfl	1.8	0.8	2844	75
matchup history	0.27	0.3	3838	33
match-up promotions	0.25	0.3	4172	82
matchup chart compilation	0.96	0.1	6377	7

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Integral ln(x) - Math2.org
math2.org

http://math2.org/math/integrals/more/ln.htm

ln(x) dx set u = ln(x), dv = dx then we find du = (1/x) dx, v = x substitute ln(x) dx = u dv and use integration by parts = uv - v du substitute u=ln(x), v=x, and du=(1/x)dx = ln(x) x - x (1/x) dx = ln(x) x - dx = ln(x) x - x + C = x ln(x) - x + C. Q.E.D.

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e and ln - AlgebraLAB
algebralab.org

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_Exponents_e.xml

The natural logarithm (ln) Another important use of e is as the base of a logarithm. When used as the base for a logarithm, we use a different notation. Rather than writing we use the notation ln(x).This is called the natural logarithm and is read phonetically as “el in of x”. Just because it is written differently does not mean we treat it differently than other logarithms.

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microsoft.com

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