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The integral \(\int \frac{\left(2x-1\right)\cos \sqrt{(2x-1{)}^{2}+5}}{\sqrt{4{x}^{2}-4x+6}}dx\) is equal to: (where c i…

Q1

The integral \(\int \frac{\left(2x-1\right)\cos \sqrt{(2x-1{)}^{2}+5}}{\sqrt{4{x}^{2}-4x+6}}dx\) is equal to: (where c is a constant of integration)

[JEE Main 2021, 18 Mar (Shift 1)]

a

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

b

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

c

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

d

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

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