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Home Exponential and Logartihmic Functions Methods of Integrations Examples Example 11
 
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Example 11

∫ x ln x dx.

Try u = ln x, dv = x dx. Then

du = 1/x dx, v = x2/2,

08_exp-log_functions-592.gif

We give two more clues and illustrate them with examples. EXAMPLE 12 ∫ (ln x)2 dx. Put u = (ln x)2, dv = dx. Then

08_exp-log_functions-593.gif

Clue: Sometimes u = f(x), dv = dx can be used to evaluate an integral ∫ f(x) dx by parts.

Clue: Sometimes one can perform two integrations by parts and solve for the desired integral.
Home Exponential and Logartihmic Functions Methods of Integrations Examples Example 11

Last Update: 2006-11-15