collard greens soup with beans | Integral ln(x)

Keyword	CPC	PCC	Volume	Score	Length of keyword
collard greens soup with beans	1.94	0.5	6143	61	30
collard	0.41	0.9	7983	61	7
greens	0.81	1	9489	1	6
soup	0.34	0.7	6116	54	4
with	1.3	0.4	6050	57	4
beans	1.6	1	2102	99	5

Keyword	CPC	PCC	Volume	Score
collard greens soup with beans	0.16	0.5	1558	93
collard greens soup with white beans	1.56	0.7	7251	6
collard greens and beans soup	1.28	0.8	1195	15
collard green soup with ham and beans	0.52	0.9	2087	40
white bean and collard green soup with rice	1.33	0.1	143	37

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Integral ln(x) - Math2.org
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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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Integral ln(x) - math
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http://www.math.com/tables/integrals/more/ln.htm

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e and ln - AlgebraLAB
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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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