Question

Evaluate: $\int (3e^{3x}+e^{-x})dx$

• A. $e^{3x}+e^{-x}+C$
• B. $e^{3x}-e^{-x}+C$
• C. $e^{3x}+e^{-2x}+C$
• D. $3e^{3x}+e^{-x}+C$

Answer 1

The correct option is B $e^{3x}-e^{-x}+C$

$\int (3e^{3x}+e^{-x})dx$

$=\int 3e^{3x}dx+\int e^{-x}dx$

$=\frac{3e^{3x}}{3}+\frac{e^{-x}}{-1}+C$

$=e^{3x}-e^{-x}+C$