# Math Help - Integration involving ln

1. ## Integration involving ln

$\int 7x ln (2x) dx$

Could any please tell me what to set as my dv, u, v and du?

2. Originally Posted by Archduke01
$\int 7x ln (2x) dx$

Could any please tell me what to set as my dv, u, v and du?
What do you think?
Actually If we assume $dv=ln(2x)dx$, What will happen?
How will find v in that case ?
And suggest to take $v=?$

3. Originally Posted by Miss
What do you think?
Actually If we assume $dv=ln(2x)dx$, What will happen?
How will find v in that case ?
And suggest to take $v=?$
Well clearly we would need to get the integral of dv. I know the integral of ln x is x ln x - x + C, but what would it be considering that it's 2x in our problem?

4. Originally Posted by Archduke01
Well clearly we would need to get the integral of dv. I know the integral of ln x is x ln x - x + C, but what would it be considering that it's 2x in our problem?
And this becomes by using integration by parts !
You will make integration by parts to find your v.
then you will do integration by parts for the main integral!

This suggest to take $dv=7xdx$ and $u=ln(2x)$

For your question about $\int ln(2x) \, dx \,\$ :
Spoiler:

$ln(2x)=ln(2)+ln(x)$.

5. Originally Posted by Miss
And this becomes by using integration by parts !
You will make integration by parts to find your v.
then you will do integration by parts for the main integral!

This suggest to take $dv=7xdx$ and $u=ln(2x)$

For your question about $\int ln(2x) \, dx \,\$ :
Spoiler:

$ln(2x)=ln(2)+ln(x)$.

Thank you for the detailed response, daddy-o. And you're right, it's actually easier if you set dv as 7x.