Chapter 4, Problem 1RE

Finding an Indefinite Integral In Exercises 1-8, find the indefinite integral.

${\displaystyle \int (x^3+4)dx}$

To determine

To calculate: The value of the indefinite integral ${\displaystyle \int \left(x^3+4\right)dx}$.

Answer to Problem 1RE

Solution:

The indefinite integral equals $\underset{¯}{\frac{x^4}{4}+4x+c}$.

Explanation of Solution

Formula Used:

The following integration formula holds:

${\displaystyle \int x^{k}dx}=\frac{x^{k+1}}{k+1}+c$

Calculation:

The indefinite integral can be computed as:

$\begin{array}{c}{\displaystyle \int \left(x^3+4\right)dx}={\displaystyle \int x^{3}dx}+{\displaystyle \int 4dx}\\ =\frac{x^4}{4}+4x+c\end{array}$

Hence, The indefinite integral equals $\frac{x^4}{4}+4x+c$.