find ∫(8x³ + 8x² - 9x + 2) dx. ∫(8x³ + 8x² - 9x + 2) dx = □

Explanation:

Step1: Apply sum - rule of integration

$\int(8x^{3}+8x^{2}-9x + 2)dx=\int8x^{3}dx+\int8x^{2}dx-\int9xdx+\int2dx$

Step2: Use power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$)

For $\int8x^{3}dx$, $8\times\frac{x^{3 + 1}}{3+1}=2x^{4}$; for $\int8x^{2}dx$, $8\times\frac{x^{2+1}}{2 + 1}=\frac{8}{3}x^{3}$; for $\int9xdx$, $9\times\frac{x^{1+1}}{1+1}=\frac{9}{2}x^{2}$; for $\int2dx$, $2x$.

Step3: Combine the results

$2x^{4}+\frac{8}{3}x^{3}-\frac{9}{2}x^{2}+2x + C$

Answer:

$2x^{4}+\frac{8}{3}x^{3}-\frac{9}{2}x^{2}+2x + C$