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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1
If F(x)=∫0xln⁡(1−t1+t)dtF(x)=\int\limits_{0}^x \ln \left(\frac{1-t}{1+t}\right) d t, then F′(−x)+F′(x)F^{\prime}(-x)+F^{\prime}(x) equals
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Correct option: A
0
Option A (0) is correct because F′(x)F'(x) is the derivative of the integral, and F′(−x)+F′(x)F'(-x) + F'(x) simplifies to 0 due to the properties of logarithms.

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