Question

Evaluate the following integral. e^x+3/e^x g

Answer 1

Answer:

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

Step-by-step explanation:

Given the integral $\int\limits {\dfrac{e^{x}+3}{e^x} } \, dx$, we are to evaluate it. Note that sum of integral is equal to the integral of its individual sum as  shown;

$\int\limits {\dfrac{e^{x}+3}{e^x} } \, dx = \int\limits {\dfrac{e^{x}}{e^x} } \, dx + \int\limits {\dfrac{3}{e^x} } \, dx$

$= \int\limits 1\, dx + 3\int\limits {e^{-x} \, dx$

$= x + 3(-e^{-x})\\\\= x -3e^{-x} + C$

Hence the value of the evaluated integral is $x -3e^{-x} + C$ where C is the constant of integration.