question\ncalculate the integral and write the answer in simplest form.\n int (6 - 5x) dx

Explanation:

Step1: Apply integral rules

Use $\int (a + b)dx=\int adx+\int bdx$. So $\int(6 - 5x)dx=\int 6dx-\int 5xdx$.

Step2: Integrate each term

For $\int 6dx$, since $\int kdx=kx + C$ ($k$ is a constant), $\int 6dx = 6x$. For $\int 5xdx$, using $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), here $n = 1$, so $\int 5xdx=5\times\frac{x^{2}}{2}=\frac{5x^{2}}{2}$.

Step3: Combine results

$\int(6 - 5x)dx=6x-\frac{5x^{2}}{2}+C$.

Answer:

$6x-\frac{5x^{2}}{2}+C$