Subjects calculus

Integrate Linear

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Integrate Linear


1. We need to find the integral of the function $2x - 6$ with respect to $x$. 2. The integral of $2x$ is calculated as $$\int 2x \, dx = 2 \cdot \frac{x^2}{2} = x^2.$$ 3. The integral of $-6$ is $$\int -6 \, dx = -6x.$$ 4. Combine the results from steps 2 and 3 to get $$\int (2x - 6) \, dx = x^2 - 6x + C,$$ where $C$ is the constant of integration. 5. Hence, the indefinite integral of the function $2x - 6$ is $$x^2 - 6x + C.$$