Question:
If
$$
\int \frac{x^2 - x + 2}{x^2 + x + 2} dx = x - \log(f(x)) + \frac{2}{\sqrt{7}} \tan^{-1}(g(x)) + c,
$$
then find
$$
f(-1) + \sqrt{7} g(-1).
$$
If
$$
\int \frac{x^2 - x + 2}{x^2 + x + 2} dx = x - \log(f(x)) + \frac{2}{\sqrt{7}} \tan^{-1}(g(x)) + c,
$$
then find
$$
f(-1) + \sqrt{7} g(-1).
$$
Show Hint
Evaluate integral parts and substitute given value.
Updated On: Jun 4, 2025
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The Correct Option is A
Solution and Explanation
From the integral form, compare and find \( f(x) \) and \( g(x) \). Evaluate at \( x = -1 \), compute \( f(-1) \) and \( g(-1) \). Sum: \[ f(-1) + \sqrt{7} g(-1) = 1 \]
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