Question

$\int \frac{1}{x^{4}} d x$\int \frac{1}{x^{4}} d x

Answer 1

$\int\frac{1}{x^4}dx$

We can find the integral using the following properties:

$\begin{gathered} a^{-n}=\frac{1}{a^n} \\ \int x^ndx=\frac{x^{n+1}}{n+1} \end{gathered}$

So:

$\begin{gathered} \int\frac{1}{x^4}dx=\int x^{-4}dx=\frac{x^{-4+1}}{-4+1}=\frac{x^{-3}}{-3}=-\frac{1}{3x^3} \\ Answer: \\ -\frac{1}{3x^3} \end{gathered}$