Improper Integration of (1/x)(lnx)^2: Troubleshooting and Correct Solutions

[st3dent]

I don't know what I'm doing wrong when taking this simple integral.

The integral is:

$$\int$$ (1/x)(lnx)^2 dx

$$\int$$ (2/x)(lnx) dx

2$$\int$$ (lnx/x) dx

Let u = lnx
du/dx = 1/x
dx = xdu

2$$\int$$ (u/x) xdu

2$$\int$$ (u) du

2$$\int$$ (u^2)/2 + C

(2(lnx)^2)/2 + C

(lnx)^2 + C

The answer is obviously wrong...how do i solve this properly?

 

[cookiemonster]

Try the substitution u = lnx.

cookiemonster

 

[HallsofIvy]

I don't know what I'm doing wrong when taking this simple integral.

The integral is:

$$\int$$ (1/x)(lnx)^2 dx

$$\int$$ (2/x)(lnx) dx

How did you make that step? ln(x²)= 2ln(x)
but this is (ln(x))².

Just go ahead and make the substitution u= ln(x) right at the start.

 

[st3dent]

thanks

Thanks..seems to work now. I got it. Thanks for all your help.