Integral of log x^2/(log x^2 + log (c - x)^2) over a range symmetric about c/2

The same question, asked 2 times: 21 Apr 2025 S1*, 25 Apr 2025 S1. Every wording below, oldest first.

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Question 1
21 Apr 2025 S1
113 $\int_{2}^{4} \frac{\log x^{2}}{\log x^{2}+ \log\left( 36 - 12x+x^{2} \right)}dx$
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Question 2
25 Apr 2025 S1
108 $\int_{1}^{3} \frac{\log x^{2}}{\log\left( 16x^{2}- 8x^{3}+x^{4} \right)}dx=$
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