Question

find the following indefinite integral.
int x ^ { - 9 } d x
int x ^ { - 9 } d x =

Explanation:

Step1: Apply power - rule for integration

The power - rule for integration is \(\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C\), where \(n
eq - 1\) and \(C\) is the constant of integration. For the integral \(\int x^{-9}dx\), here \(n=-9\).

Step2: Calculate the integral

Substitute \(n = - 9\) into the power - rule formula. We get \(\frac{x^{-9 + 1}}{-9+1}+C=\frac{x^{-8}}{-8}+C\).

Answer:

\(-\frac{1}{8x^{8}}+C\)