find ∫(9x³ + 5x² - 7x + 3) dx. ∫(9x³ + 5x² - 7x + 3) dx = □

Explanation:

Step1: Apply power - rule for integration

The power - rule for integration is $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$). For $\int9x^{3}dx$, we have $9\times\frac{x^{3 + 1}}{3+1}=\frac{9}{4}x^{4}$. For $\int5x^{2}dx$, we have $5\times\frac{x^{2+1}}{2 + 1}=\frac{5}{3}x^{3}$. For $\int(-7x)dx$, we have $-7\times\frac{x^{1+1}}{1+1}=-\frac{7}{2}x^{2}$. For $\int3dx$, we have $3x$.

Step2: Combine the results

$\int(9x^{3}+5x^{2}-7x + 3)dx=\frac{9}{4}x^{4}+\frac{5}{3}x^{3}-\frac{7}{2}x^{2}+3x + C$

Answer:

$\frac{9}{4}x^{4}+\frac{5}{3}x^{3}-\frac{7}{2}x^{2}+3x + C$