example 1 find each indefinite integral. a. ∫ 1/2 dx b. ∫ 1dx c. ∫ -5dx

Explanation:

Step1: Recall integral rule

The integral of a constant $k$ with respect to $x$ is $kx + C$, where $C$ is the constant of integration.

Step2: Solve part a

For $\int\frac{1}{2}dx$, using the rule $\int kdx=kx + C$ with $k = \frac{1}{2}$, we get $\frac{1}{2}x + C$.

Step3: Solve part b

For $\int 1dx$, using the rule $\int kdx=kx + C$ with $k = 1$, we get $1\times x+C=x + C$.

Step4: Solve part c

For $\int - 5dx$, using the rule $\int kdx=kx + C$ with $k=-5$, we get $-5x + C$.

Answer:

a. $\frac{1}{2}x + C$ b. $x + C$ c. $-5x + C$