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Solve the following.
If ∫ log 2x dx = x log 2x - k + c where k is a function of x, then find k.
If $\int \log 2x \, dx = x \log 2x - k + c$ where $k$ is a function of $x$, then find $k$.
Answer
Answer
$\int \log 2x \, dx = \log 2x \cdot x - \int x \cdot \frac{1}{x} \, dx$
$= x \log 2x - x + c$
Comparing with $x \log 2x - k + c$, $k = x$.
Final answer: $x$