Question

find the following indefinite integral.
$$ int x ^ { - 6 } d x $$
$$ int x ^ { - 6 } d x = $$

Explanation:

Step1: Apply the 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 \(\int x^{-6}dx\), here \(n=-6\).

Step2: Substitute \(n=-6\) into the power - rule formula

Substituting \(n = - 6\) into \(\frac{x^{n + 1}}{n+1}+C\), we get \(\frac{x^{-6 + 1}}{-6+1}+C\).
Simplify the exponent and the denominator: \(\frac{x^{-5}}{-5}+C=-\frac{1}{5x^{5}}+C\)

Answer:

\(-\frac{1}{5x^{5}}+C\)