Chapter 5, Problem 1RE

Finding an Indefinite Integral In Exercises 1-6, find the indefinite integral.

${\displaystyle \int (4x^2+x+3)dx}$

To determine

To calculate: The indefinite integral of the given function $f\left(x\right)=4x^2+x+3$.

Answer to Problem 1RE

Solution:

The value of integral of the given function is $\underset{\_}{\frac{8x^3+3x^2+18x}{6}+c}$.

Explanation of Solution

Given:

Function is: $f\left(x\right)=4x^2+x+3$

Formula used:

Integral property as: ${\displaystyle \int x^{n}x=\frac{x^{n+1}}{n+1}}+c$

Calculation:

Solve the integral as:

$\begin{array}{ccc}\hfill {\displaystyle \int f\left(x\right)dx}& =& {\displaystyle \int \left(4x^2+x+3\right)}dx\hfill \\ \hfill & =& {\displaystyle \int 4x^{2}dx+{\displaystyle \int xdx+{\displaystyle \int 3dx}}}\hfill \\ \hfill & =& \frac{8x^3+3x^2+18x}{6}+c\hfill \end{array}$

Thus, the value of integral of the given function is $\frac{8x^3+3x^2+18x}{6}+c$.