Question

find the general indefinite integral. (use c for the constant of the indefinite integral.) ( int 28x^3 , dx )

Explanation:

Step1: Use the power rule for integration

The power rule for integration states that $\int x^n dx = \frac{x^{n + 1}}{n + 1} + C$ (where $n
eq -1$) and the constant multiple rule which says $\int kf(x)dx = k\int f(x)dx$ for a constant $k$. For the integral $\int 28x^3 dx$, we can factor out the constant 28 first. So we have $28\int x^3 dx$.

Step2: Apply the power rule

Using the power rule with $n = 3$, we get $\int x^3 dx=\frac{x^{3 + 1}}{3 + 1}+C=\frac{x^4}{4}+C$. Then multiply by the constant 28: $28\times\frac{x^4}{4}+C$.

Step3: Simplify the expression

Simplify $28\times\frac{x^4}{4}$. We can divide 28 by 4: $\frac{28}{4} = 7$. So the expression becomes $7x^4 + C$.

Answer:

$7x^4 + C$