The integral in the image appears to be:

$\int \frac{dx}{\sin(x) \cos(x)}$

This integral can be simplified by using a trigonometric identity. Recall that:

$\sin(2x) = 2 \sin(x) \cos(x)$

Thus, we can rewrite the integrand as:

$\frac{1}{\sin(x) \cos(x)} = \frac{2}{\sin(2x)}$

This simplifies the integral to:

$\int \frac{dx}{\sin(x) \cos(x)} = 2 \int \frac{dx}{\sin(2x)}$

The integral of $\frac{1}{\sin(2x)}$ is known, and it is the logarithmic form:

$\int \frac{dx}{\sin(2x)} = -\frac{1}{2} \ln|\cot(2x)|$

Thus, the final result of the original integral is:

$\int \frac{dx}{\sin(x) \cos(x)} = -\ln|\cot(x)| + C$

where $C$ is the constant of integration.

Would you like more details on any part of the solution?

Here are some related questions for further exploration:

1. How can other trigonometric identities help simplify similar integrals?
2. What is the integral of $\frac{1}{\cos^2(x)}$?
3. How can substitution methods simplify trigonometric integrals?
4. Can the integral of $\frac{1}{\sin^2(x)}$ be calculated similarly?
5. What is the relationship between logarithmic functions and trigonometric integrals?

Tip: Always look for ways to simplify trigonometric expressions using identities like double-angle formulas!