Answer:
[tex]x -3e^{-x} + C[/tex]
Step-by-step explanation:
Given the integral [tex]\int\limits {\dfrac{e^{x}+3}{e^x} } \, dx[/tex], we are to evaluate it. Note that sum of integral is equal to the integral of its individual sum as shown;
[tex]\int\limits {\dfrac{e^{x}+3}{e^x} } \, dx = \int\limits {\dfrac{e^{x}}{e^x} } \, dx + \int\limits {\dfrac{3}{e^x} } \, dx[/tex]
[tex]= \int\limits 1\, dx + 3\int\limits {e^{-x} \, dx \\\\[/tex]
[tex]= x + 3(-e^{-x})\\\\= x -3e^{-x} + C[/tex]
Hence the value of the evaluated integral is [tex]x -3e^{-x} + C[/tex] where C is the constant of integration.
