## Integral of (x + 1/x) * ln(x) dx

Limits, differentiation, related rates, integration, trig integrals, etc.
mitnord
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### Integral of (x + 1/x) * ln(x) dx

Help me solve the integral of (x + 1/x) * ln(x) dx

Keep going in circles, Calculus 1. semester.

Thank you.

stapel_eliz
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mitnord wrote:Keep going in circles

What were the "circles"? (You'd be surprised how often an apparent "circle" is actually leading to the solution!)

mitnord wrote:Help me solve the integral of (x + 1/x) * ln(x) dx

It might help to break this into two integrals:

. . . . $I_1\, =\, \int\, x\ln(x)\, dx\, \mbox{ and }\, I_2\, =\, \int\, \frac{1}{x}\ln(x)\, dx$

The second integral, I2, should be simple enough. It's the other one that's a bit of a bear. I would suggest integration by parts, with:

. . . . $u\, =\, \ln(x)\, \mbox{ and }\, dv\, =\, x\, dx$

Hope that helps!

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