Calculus Integration of tln(t)dt: Homework Exercise and Methods

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SUMMARY

The integral of the function tln(t)dt can be effectively solved using integration by parts. The correct approach involves setting u as ln(t) and dv as t dt, which simplifies the integration process. The initial attempt to set u as t and v as 1/x is incorrect, as the antiderivative of ln(t) is not 1/t. By correctly applying the integration by parts formula, the integral can be resolved efficiently.

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Homework Statement


Integrate the following:


Homework Equations


tln(t)dt


The Attempt at a Solution



if i do intergration by parts:
u=t
u'=1
v'=ln(t)
v=1/x
and then use the formule, would that give me a correct answer?
Is there a simpler way?
 
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The antiderivative of ln(t) is not 1/t. That's the derivative.

When you have both a logarithm and polynomial term, make u the log term and dv be the polynomial.
 
Switch your substitutions, and it's solved.
 

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