Evaluate the indefinite integral: $\int 4x dx$

• A. $2x^2+C$
• B. $9x^4+C$
• C. $4.5x^2+C$
• D. $36x+C$

Answer: (A)

Verified step by step guidance

1. Step 1: Identify the integral to be solved. The problem asks to evaluate the indefinite integral of 9 * 4x with respect to x, which can be written as ∫ 9 * 4x dx.
2. Step 2: Simplify the integrand. Combine the constants 9 and 4 to get 36, so the integral becomes ∫ 36x dx.
3. Step 3: Apply the power rule for integration. The power rule states that ∫ x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1. Here, the exponent of x is 1.
4. Step 4: Increase the exponent of x by 1 (from 1 to 2) and divide by the new exponent. This gives (36x^2)/2 + C.
5. Step 5: Simplify the result. Divide 36 by 2 to get 18, so the final expression becomes 18x^2 + C.