It seems you've uploaded a math problem related to integration by parts. Let's go through it step by step.

The integral is:

$\int_1^7 \frac{(\ln(x))^2}{x^3} \, dx$

The problem asks for the steps in performing integration by parts. Based on your description, we'll need to determine the appropriate choices for $u$, $dv$, $du$, and $v$, and then proceed to evaluate the integral.

First Integration by Parts Setup:

Given the choice:

$u = (\ln(x))^2$

Then, we can differentiate $u$ to find $du$:

$du = \frac{d}{dx} \left( (\ln(x))^2 \right)$

We use the chain rule:

$du = 2 \ln(x) \cdot \frac{1}{x} \, dx$

Next, for $dv$, we have the remaining part of the integrand:

$dv = \frac{1}{x^3} \, dx$

Integrating $dv$:

$v = \int \frac{1}{x^3} \, dx = \frac{-1}{2x^2}$

Second Integration by Parts Setup:

For the second integration by parts, the integral to solve becomes:

$\int_1^7 v \, du = \int_1^7 \frac{-1}{2x^2} \cdot 2 \ln(x) \cdot \frac{1}{x} \, dx$

This simplifies to:

$\int_1^7 \frac{-\ln(x)}{x^3} \, dx$

Let's go ahead and finish this step.

Would you like me to continue and solve the integral or clarify any part of the process? Feel free to ask!