Questions: Calculate the following indefinite integral (make sure you include +C as part of your answer). ∫ x dx = □

Calculate the following indefinite integral (make sure you include +C as part of your answer).
∫ x dx = □

Transcript text: Section 4.9: Problem 1 (1 point) Directions: Calculate the following indefinite integral (make sure you include $+C$ as part of your answer). \[ \int x d x=\square \] Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining.

Solution

Solution Steps

Step 1: Identify the integral

The given integral is: \[ \int x \, dx \]

Step 2: Apply the power rule for integration

The power rule for integration states that: \[ \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \] where \( n \neq -1 \). In this case, \( n = 1 \).

Step 3: Compute the integral

Applying the power rule: \[ \int x \, dx = \frac{x^{1+1}}{1+1} + C = \frac{x^2}{2} + C \]

Final Answer

\[ \boxed{\int x \, dx = \frac{x^2}{2} + C} \]

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