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Question:

∫2x+5√(7-6x-x²)dx = A√(7-6x-x²) + Bsin⁻¹(x+3/4) + C (where C is a constant of integration), then the ordered pair (A,B) is equal to (2,1), (2,-1), (-2,1), (-2,-1)

(2,-1)

(-2,1)

(2,1)

(-2,-1)

Solution:

Note that 7-6x-x² = 16-(x+3)² and d/dx(7-6x-x²) = -6x-2x = -2(3+x)
So, we have
∫2x+5√(7-6x-x²)dx = ∫2x+6√(7-6x-x²)dx - ∫1√(16-(x+3)²)dx = -2√(7-6x-x²) - sin⁻¹((x+3)/4) + C
So, we have A=-2, B=-1. Thus option D is the correct answer.