What is the integral of #(ln(xe^x))/x#?
2 Answers
Explanation:
We are given:
Using
Using
Using
Splitting the fraction (
Separating the summed integrals:
The second integral is simply
Let
Using
Integrating (the arbitrary constant
Substituting back in terms of
Explanation:
We begin by using the following logarithm identity:
Applying this to the integral, we get:
To evaluate the remaining integral, we use integration by parts:
I will let
We can then apply the integration by parts formula to get:
Since we have the integral on both sides of the equals sign, we can solve it like an equation:
Plugging back into the original expression, we get our final answer: