If $\int \frac{2\cos x - \sin x + \lambda}{\cos x + \sin x + 2} dx = A\ln|\cos x + \sin x - 2| + Bx + C$. Then the value of $A + B + |\lambda|$ is
Step-by-Step Solution
Key Concept: Differentiate the antiderivative form and match coefficients with the given expression to identify unknown constants.
To find constants in $\frac{d}{dx}(A\ln|\cos x + \sin x - 2| + Bx + C) = A\frac{\cos x - \sin x}{\cos x + \sin x - 2} + B$, match this with the given derivative. From coefficient matching: $2 = A + B$, $-1 = -A + B\lambda$, and $-2 = -2B$, yielding $B = 1$, $A = 1$, and $\lambda = -1$.
Correct Answer: 2