Examples of indefinite integrals for polynomial expressions typically found in Calculus I homework.

I'll solve these three indefinite integrals step by step.

## Problem 13: ∫(3x - 9x - 3)dx

Step 1: Apply the power rule to each term separately
- Power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1) + C

Step 2: Integrate each term
- ∫3x⁴ dx = 3 · x⁵/5 = (3/5)x⁵
- ∫-9x dx = -9 · x²/2 = -(9/2)x²
- ∫-3 dx = -3x

Step 3: Combine and add constant of integration
Result: (3/5)x⁵ - (9/2)x² - 3x + C

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## Problem 15: ∫(4x⁵ + 8x - 9)dx

Step 1: Apply the power rule to each term

Step 2: Integrate each term
- ∫4x⁵ dx = 4 · x⁶/6 = (4/6)x⁶ = (2/3)x⁶
- ∫8x dx = 8 · x²/2 = 4x²
- ∫-9 dx = -9x

Step 3: Combine and add constant of integration
Result: (2/3)x⁶ + 4x² - 9x + C

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## Problem 17: ∫(4x³ + 3x - 2)dx

Step 1: Apply the power rule to each term

Step 2: Integrate each term
- ∫4x³ dx = 4 · x⁴/4 = x⁴
- ∫3x dx = 3 · x²/2 = (3/2)x²
- ∫-2 dx = -2x

Step 3: Combine and add constant of integration
Result: x⁴ + (3/2)x² - 2x + C

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Final Answer:
13) (3/5)x⁵ - (9/2)x² - 3x + C

15) (2/3)x⁶ + 4x² - 9x + C

17) x⁴ + (3/2)x² - 2x + C