Question

Evaluate: $\int \sqrt[9]{9x^{-8}}dx$

• A. $9x^{\frac{1}{9}}+c$
• B. $9x^{\frac{8}{9}}+c$
  
• C. $x^{\frac{1}{9}}+c$
  
• D. $x^{\frac{8}{9}}+c$
  

Answer 1

The correct option is A $9x^{\frac{1}{9}}+c$

$\int (x^{-8}{)}^{1/9}dx=\int x^{-8/9}dx=\frac{x^{-8/9+1}}{-8/9+1}+c=9x^{1/9}+c$