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Multiple Choice
Evaluate the indefinite integral:
A
B
C
D
Verified step by step guidance
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Step 1: Recall the formula for the indefinite integral of a polynomial term. For a term of the form ax^n, the integral is (a/(n+1))x^(n+1) + C, where C is the constant of integration.
Step 2: Break the given polynomial into individual terms: 2x^2, 3x, and 1. Each term will be integrated separately.
Step 3: Apply the integration formula to the first term, 2x^2. The integral of 2x^2 is (2/(2+1))x^(2+1) = (2/3)x^3.
Step 4: Apply the integration formula to the second term, 3x. The integral of 3x is (3/(1+1))x^(1+1) = (3/2)x^2.
Step 5: Apply the integration formula to the constant term, 1. The integral of 1 is x. Combine all the results to form the final expression: (2/3)x^3 + (3/2)x^2 + x + C.