question\ncalculate the integral and write the answer in simplest form.\n int (-3x^{5}+2)dx

Explanation:

Step1: Apply sum - rule of integration

$\int(-3x^{5}+2)dx=\int(-3x^{5})dx+\int 2dx$

Step2: Integrate each term

For $\int(-3x^{5})dx$, using the power - rule $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), we have $\int(-3x^{5})dx=-3\int x^{5}dx=-3\times\frac{x^{5 + 1}}{5+1}=-\frac{1}{2}x^{6}$. For $\int 2dx$, since $\int kdx=kx + C$ ($k$ is a constant), $\int 2dx=2x$.

Step3: Combine the results

$-\frac{1}{2}x^{6}+2x + C$

Answer:

$-\frac{1}{2}x^{6}+2x + C$