https://file.aiquickdraw.com/mathbot/file/1729589161540m5udh5mc.jpg

The given expression in the image is an integral:

\[
\int \tan(x) \, dx
\]

The integral of \(\tan(x)\) with respect to \(x\) is:

\[
\int \tan(x) \, dx = -\ln|\cos(x)| + C
\]

where \(C\) is the constant of integration.

Would you like further details or any additional clarifications?

Here are some related questions to expand on this:

1. How is the integral of \(\tan(x)\) derived?
2. What is the integral of \(\sec(x)\), which is closely related to \(\tan(x)\)?
3. Can we use substitution to solve integrals like \(\int \tan(x) \, dx\)?
4. How is the logarithmic function involved in the integration of trigonometric functions?
5. What are other common integrals of trigonometric functions?

**Tip**: Always remember that logarithmic functions often arise when integrating trigonometric functions like \(\tan(x)\) due to their derivative properties.

What is the integral of the given expression Stgx dx?

Learn how to solve the integral of tan(x) with respect to x. This solution covers key calculus concepts, including trigonometric function integration and logarithmic functions. Suitable for students in Grades 11-12.

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