Certainly! Here is a challenging integral problem for you:

Evaluate the integral:

\[
\int_0^1 \ln(1 + x^2) \, dx
\]

Would you like to see the detailed solution or have any questions about this problem? 

Here are 8 related questions to expand your understanding:

1. How do you generally approach the evaluation of definite integrals involving logarithmic functions?
2. Can you find the integral of \(\ln(1 + x^2)\) over different limits, such as \([1, 2]\)?
3. What techniques are useful for integrals involving natural logarithms?
4. How can integration by parts be applied to integrals with logarithmic functions?
5. What are some properties of the natural logarithm function that can simplify integration?
6. Can you evaluate \(\int \ln(1 + x^2) \, dx\) without specified limits?
7. How does the substitution method help in solving integrals involving logarithms?
8. Are there any specific applications of integrals involving logarithmic functions in real-world problems?

**Tip:** When evaluating definite integrals, always check if the function has any properties (such as symmetry) that can simplify the calculation.

Explore the evaluation of the integral of ln(1 + x^2) from 0 to 1 with a detailed step-by-step solution. This problem covers advanced topics in integration and logarithmic functions, suitable for advanced high school students and above.

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