find the integral.\n int\frac{1}{x^{10}}dx \n int\frac{1}{x^{10}}dx=square

Explanation:

Step1: Rewrite the integrand

Rewrite $\frac{1}{x^{10}}$ as $x^{- 10}$. So the integral becomes $\int x^{-10}dx$.

Step2: Apply power - rule for integration

The power - rule for integration is $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$). Here $n=-10$, so $\int x^{-10}dx=\frac{x^{-10 + 1}}{-10 + 1}+C$.

Step3: Simplify the result

$\frac{x^{-9}}{-9}+C=-\frac{1}{9x^{9}}+C$.

Answer:

$-\frac{1}{9x^{9}}+C$