INTEGRATION OF LOG X

We can integrate logx using the method integration by parts.

The formula for integration by parts :

∫udv = uv - ∫vdu

Integration of logx is

∫logxdx

In ∫logxdx, consider logx as u and dx as dv.

That is,

u = logx

dv = dx

Find du and v.

∫logxdx = uv - ∫vdu

Substitute u = lox, v = x and du = (1/x)dx.

∫logxdx = (logx)(x) - ∫(x)(1/x)dx

∫logxdx = xlogx - ∫dx

∫logxdx = xlogx - x + c

∫logxdx = x(logx - 1) + c

So, integration of lox is equal to x(logx - 1) + c.

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