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
Explanation
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
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