If ∫x3+x2+x15+12x+10x2dx=g(x)k15+12x+10x2+C\int \frac{x^3 + x^2 + x}{\sqrt{15 + 12x + 10x^2}} dx = \frac{g(x)}{k} \sqrt{15 + 12x + 10x^2} + C…

Mathematics

Problem

If ∫x3+x2+x15+12x+10x2dx=g(x)k15+12x+10x2+C\int \frac{x^3 + x^2 + x}{\sqrt{15 + 12x + 10x^2}} dx = \frac{g(x)}{k} \sqrt{15 + 12x + 10x^2} + C where C is the constant of integration and g(1)=1g(1) = 1 then (g′(1)+g′′(1)+k)(g'(1) + g''(1) + k) is equal to : (A) 30 (B) 32 (C) 34 (D) 36

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