Question

Find the integral of \( 2x + 1 \).

• A. \( \frac{2x+1}{\log 2} + k \)
• B. \( 2x + 1 \log 2 + k \)
• C. \( (x+1)^2 + k \)
• D. \( 2x + 1 + k \)

Hint:

The integral of a linear function like \( 2x + 1 \) is straightforward using basic power rules.

Answer 1

The Correct Option is A

We are asked to find the integral of \( 2x + 1 \). The general rule for integrating \( ax^n \) is \( \frac{a}{n+1} x^{n+1} \). For this question, the integral is as follows: \[ \int (2x + 1) \, dx = x^2 + x + k. \] Thus, the final result is \( x^2 + x + k \).