How to integrate (ln x)(squared)

[Curious6]

Hi,

I've been struggling with this problem for hours, so I was wondering if someone here could help me out, thanks:

The problem is:

How to integrate: (ln x)(to the power of 2)

Thanks

 

[amcavoy]

Hi,

I've been struggling with this problem for hours, so I was wondering if someone here could help me out, thanks:

The problem is:

How to integrate: (ln x)(to the power of 2)

Thanks

$$\int\left(\ln{x}\right)^{2}\,dx=x\left(\ln{x}\right)^{2}-2\int\ln{x}\,dx$$

$$\int\ln{x}\,dx=x\ln{x}-x$$

I just used part-integration:

$$\int v\,du=uv-\int u\,dv$$

...You should be able to put it together from here.

 

[Curious6]

Ok, I understand now, thanks