The given mathematical expression appears to be an integral:

$\int_a^{a+l} k_e \lambda \frac{dx}{x^2}$

Where:

• $k_e$ and $\lambda$ are constants.
• The integral is taken from $a$ to $a + l$, and the function to integrate is $\frac{dx}{x^2}$.

To solve this, let's first consider the general form of the integral:

$\int \frac{dx}{x^2} = -\frac{1}{x} + C$

Now, applying the limits of integration from $a$ to $a + l$:

$\int_a^{a+l} \frac{dx}{x^2} = \left[ -\frac{1}{x} \right]_a^{a+l} = -\frac{1}{a+l} + \frac{1}{a}$

Thus, the solution to the given integral becomes:

$\int_a^{a+l} k_e \lambda \frac{dx}{x^2} = k_e \lambda \left( \frac{1}{a} - \frac{1}{a+l} \right)$

This is the evaluated result of the integral.

Would you like further explanation or details on any step?

Here are five related questions to expand your understanding:

1. What is the physical or theoretical context of this integral involving $k_e$ and $\lambda$?
2. How does the result change if $\lambda$ is not constant but a function of $x$?
3. Can you generalize this result for higher powers of $x$ in the denominator?
4. What is the impact of changing the limits of integration on the final result?
5. How would this integral be solved if it included additional terms in the denominator?

Tip: When working with definite integrals, always check the limits carefully to avoid sign errors.