Question

Find the general indefinite integral. Use C for the constant of integration. Remember to use absolute values where appropriate

Answer 1

ANSWER

$e^x\text{ + }\frac{1}{3}\ln (|x|)\text{ + C}$

EXPLANATION

Given:

$\int (e^x\text{ + }\frac{1}{3x})dx$

Integrating the expression:

$\begin{gathered} =\int (e^x)\text{ }dx\text{+}\int (\frac{1}{3x})dx \\ =\text{ }e^x\text{ + }\frac{1}{3}\int (\frac{1}{x})dx\text{ + c} \\ =e^x\text{ + }\frac{1}{3}\ln \text{ (|x|) + C} \end{gathered}$