Question

What will be the integration of x to the power -3

Answer 1

integration of x^(-3) is x ^(-2) /-2

Answer 2

Here we will be using the identity:


$\boxed{\displaystyle \int x^n \, dx = \frac{x^{n+1}}{n+1} +c}$

So, here we would have:

 $\displaystyle \int x^{-3} \, dx \\ \\ \\ = \frac{x^{-3+1}}{-3+1} +c \\ \\ \\ = \frac{x^{-2}}{-2}+c \\ \\ \\ = -\frac{1}{2x^2}+c \\ \\ \\ \\ \implies \boxed{\int x^{-3} \, dx = -\frac{1}{2x^2}+c}$