Question

Solve:
$\int x^{-3}\left(x+1\right)dx$

• A. $-\frac{1}{2}{(1-\frac{1}{x})}^2+c$
• B. $-\frac{1}{x}(1+\frac{1}{2x})+c$
  
• C. $\frac{1}{2}{(1-\frac{1}{x})}^2+c$
  
• D. $\frac{1}{2}{(1+\frac{1}{x})}^2+c$
  

Answer 1

The correct option is B $-\frac{1}{x}(1+\frac{1}{2x})+c$

$\int \frac{x}{x^3}dx+\int \frac{1}{x^3}dx$

$\int x^{-2}dx+\int x^{-3}dx$

$-\frac{1}{x}-\frac{1}{2x^2}+C$

$-\frac{1}{x}(1+\frac{1}{2x})+C$