Question

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

Answer 1

`x -3e^(-x) + C`

Explanation:

Given the integral
`\int\limits {(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 {(e^(x)+3)/(e^x) } \, dx = \int\limits {(e^(x))/(e^x) } \, dx + \int\limits {(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.