Chapter 9.4, Problem 4QR

To determine

To find: the value of integral.

Answer to Problem 4QR

The value of integral is $-\frac{1}{3x^3}$ .

Explanation of Solution

Given information:

Theintegral is ${\displaystyle \int \frac{1}{x^4}dx}$ .

Calculation: to evaluate the integral, first use the formula of integral and simplify,

  $\begin{array}{l}{\displaystyle \int \frac{1}{x^4}dx}={\displaystyle \int x^{-4}}\text{ [simplify]}\\ {\displaystyle \int \frac{1}{x^4}dx}=\frac{x^{-4+1}}{-4+1}\text{ [}{\displaystyle \int x^n}=\frac{x^{n+1}}{n+1}]\\ {\displaystyle \int \frac{1}{x^4}dx}=-\frac{1}{3x^3}\text{ [simplify]}\end{array}$

Thus, the value is $-\frac{1}{3x^3}$ .