Question

三、find each indefinite integral:
(1) $\int 1 - x^{2}dx$

Explanation:

Step1: Use integral addition rule

$$\int(1 - x^{2})dx=\int1dx-\int x^{2}dx$$

Step2: Integrate each term

• For $\int1dx$, using $\int kdx=kx + C$ ($k = 1$), we get $x$.
• For $\int x^{2}dx$, using $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n = 2$), we get $\frac{x^{3}}{3}$.

Answer:

$x-\frac{x^{3}}{3}+C$