Final answer:
To evaluate the indefinite integrals, each term within the integral is integrated separately. The final answers include the antiderivative of each term plus a constant of integration, C.
Step-by-step explanation:
The task is to evaluate two indefinite integrals:
- For the first integral, ∑(-4x³ - x - √2) dx, we integrate term by term to find the antiderivative: -4x³ becomes -x⁴, -x becomes -x²/2, and -√2 becomes -√2x. Adding the constant of integration, C, gives us the final answer.
- The second integral, ∑(-4x³ - 2) dx, is similar: -4x³ integrates to -x⁴, -2 integrates to -2x, and we again include the constant of integration, C.
Thus, the answers are:
- ∑(-4x³ - x - √2) dx = -x⁴/4 - x²/4 - √2x + C
- ∑(-4x³ - 2) dx = -x⁴/4 - 2x + C