Simple integral, textbook seems wrong

  • Thread starter Dumbledore
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  • #1
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Homework Statement



Find the equation of the curve for which the slope is (ln x)^2/x and passes through P(1, 2)


Homework Equations





The Attempt at a Solution



Integrate (ln x)^2 = 1/2 Integral( ((ln x)^2) 2/x dx)

I get: 1/2 [((ln x)^3/3) + C]

Then solving for C, I get C=2

Then my final answer is (ln x)^3/6 + 2

The textbook says it is (ln x)^3/3 + 2.

I don't get it.
 

Answers and Replies

  • #2
21
1
How exactly did you make this integration: Integral( ((ln x)^2) 2/x dx)
you should get out [tex]\frac{2ln(x)^3}{3}[/tex]
Why did you actually put this factor 2 in the integral and divide by 2 again, I don't get why this makes sense.
 
  • #3
Defennder
Homework Helper
2,591
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Well I got [tex]\int \frac{(ln x)^2}{x} dx = \frac{1}{3} (ln x)^3 + C [/tex]. Don't see where you got that factor of 1/2 from. C = 2, so that's right.
 

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