X*ln(x) = 1/2x^2*ln(x) - 1/4*x^2 not sure how they got it

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The discussion centers on the integration of the expression 2*(x^4 + xln(x)) over the interval from 1 to 3. The key result includes the terms x^5/5 + (1/2)x^2 * ln(x) - (1/4)x^2, derived through integration by parts. The integral of x*ln(x) is identified as the challenging component, which requires applying the integration by parts technique effectively. Participants clarify the steps leading to the final expression, emphasizing the importance of understanding integration methods.

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mr_coffee
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Hello everyone!

I'm doing a line integral but I'm confused on the integration method used:

I got to integral 1 to 3 2*(x^4+xln(x) ); But they then have:
x^5/5 + 1/2x^2 * ln(x) - 1/4x^2 and I'm not sure how they got the last part, 1/2x^2 * ln(x) - 1/4x^2

Thanks!

u = x isn't what they did I don't think, and its been awhile so I'm rusty on integration XD
 
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The 'hard' part is the integral of x*ln(x). And they just integrated by parts.
 
ahh thank you
 

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