Question

$\int e^x\left(\frac{x^2+5x+7}{(x+3{)}^2}\right)dx=e^{x}f\left(x\right)+c$ then f(x) =

• A. $\frac{1}{x+3}$
  
• B. $-\frac{1}{x+3}$
  
• C. $-\left(\frac{x+2}{x+3}\right)$
  
• D. $\frac{x+2}{x+3}$

Answer 1

The correct option is D $\frac{x+2}{x+3}$

$\int e^x(\frac{x+2}{x+3}+\frac{1}{(x+3{)}^2})dx=e^x.\left(\frac{x+2}{x+3}\right)+C$