Simple integral, textbook seems wrong

[Dumbledore]

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.

 

[neo86]

How exactly did you make this integration: Integral( ((ln x)^2) 2/x dx)
you should get out \frac{2ln(x)^3}{3}
Why did you actually put this factor 2 in the integral and divide by 2 again, I don't get why this makes sense.

 

[Defennder]

Well I got \int \frac{(ln x)^2}{x} dx = \frac{1}{3} (ln x)^3 + C. Don't see where you got that factor of 1/2 from. C = 2, so that's right.