You have written an integral that likely corresponds to:

\[
\int \frac{6}{1+x^2} \, dx
\]

This is a standard integral, which can be solved using the formula for the integral of \(\frac{1}{1+x^2}\), which equals \(\arctan(x)\). Applying this to the given problem:

\[
\int \frac{6}{1+x^2} \, dx = 6 \arctan(x) + C
\]

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

Would you like further explanation, or have any specific questions on this?

Here are some related questions you might find useful:
1. How do you integrate functions of the form \(\frac{a}{1+x^2}\)?
2. What is the geometric interpretation of the \(\arctan(x)\) function?
3. How does the integral of \(\frac{1}{1+x^2}\) arise in trigonometry?
4. Can we compute definite integrals involving \(\arctan(x)\)?
5. How does \(\arctan(x)\) relate to other inverse trigonometric functions?

**Tip:** The derivative of \(\arctan(x)\) is \(\frac{1}{1+x^2}\), which is key to solving this integral.

Learn how to solve the integral of 6/(1+x^2) using calculus concepts such as the integral of inverse trigonometric functions. This detailed step-by-step solution demonstrates the application of the formula for integrating 1/(1+x^2), resulting in 6 arctan(x) + C. Suitable for students in Grades 11-12.

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