The integral f √2x + 1 DX will be?

1/3(2x + 1)^2/3 + C

1/3(2x + 1)^3/2 + C

3(2x + 1)^3/2 + C

None of these

To integrate √(2x + 1), we can use the power rule of integration and the chain rule.

Let u = 2x + 1, then du/dx = 2, and du = 2dx.

∫√(2x + 1) dx = (1/2) ∫u^(1/2) du

= (1/2) (2/3) u^(3/2) + C

= (1/3) (2x + 1)^(3/2) + C