Question

find the following indefinite integral.

int x ^ { - 6 } d x

int x ^ { - 6 } d x = square

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 \(\int x^{-6}dx\), here \(n=-6\).
Substitute \(n = - 6\) into the formula: \(\frac{x^{-6 + 1}}{-6+1}+C\).

Step2: Simplify the expression

Simplify the exponent and the denominator. \(-6 + 1=-5\), so \(\frac{x^{-5}}{-5}+C\).
We can rewrite \(x^{-5}\) as \(\frac{1}{x^{5}}\), and \(\frac{x^{-5}}{-5}+C=-\frac{1}{5x^{5}}+C\).

Answer:

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