The integral ∫((2x -1)cos√((2x - 1)^2 + 5))/(√(4x^2 - 4x + 6))dx is equal to (where c is a constant of integration)

Question

The integral

\(\int\frac{(2x-1)cos\sqrt{(2x-1)^2+5}}{\sqrt{4x^2-4x+6}}\) dx is

equal to 

(where c is a constant of integration)

(1) \(\frac 12sin\sqrt{(2x-1)^2+5}+c\)

(2) \(\frac 12cos\sqrt{(2x+1)^2+5}+c\)

(3) \(\frac 12cos\sqrt{(2x-1)^2+5}+c\)

(4) \(\frac 12sin\sqrt{(2x+1)^2+5}+c\)

Answer 1

Correct option is (1) \(\frac 12sin\sqrt{(2x-1)^2+5}+c\)