find ∫(7x³ + 10x² - 7x + 2) dx. ∫(7x³ + 10x² - 7x + 2) dx =

Explanation:

Step1: Apply sum - rule of integration

$\int(7x^{3}+10x^{2}-7x + 2)dx=\int7x^{3}dx+\int10x^{2}dx-\int7xdx+\int2dx$

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

For $\int7x^{3}dx$, $7\times\frac{x^{3 + 1}}{3+1}=\frac{7x^{4}}{4}$; for $\int10x^{2}dx$, $10\times\frac{x^{2+1}}{2 + 1}=\frac{10x^{3}}{3}$; for $\int7xdx$, $7\times\frac{x^{1+1}}{1+1}=\frac{7x^{2}}{2}$; for $\int2dx$, $2x$.

Step3: Combine the results

$\frac{7x^{4}}{4}+\frac{10x^{3}}{3}-\frac{7x^{2}}{2}+2x + C$

Answer:

$\frac{7x^{4}}{4}+\frac{10x^{3}}{3}-\frac{7x^{2}}{2}+2x + C$