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Integral of ln2x?

In: Math and Arithmetic, Calculus [Edit categories]

Answer:

I will denote an integral as \int (LaTeX).

We can let u = 2x and du = 2dx, and substitute
\int ln (2x) dx = (1/2) \int ln u du. Either using integration by parts or by memorization, this is equal to

(1/2) u ln u - u + C = (1/2)(2x ln (2x) - 2x) + C, where C is an arbitrary constant.

First answer by Rspence1234. Last edit by Rspence1234. Contributor trust: 16 [recommend contributor ]. Question popularity: 10 [recommend question].

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