Question

What is the indefinite integral of `ln(sqrt(x)) dx`?

Answer 1

`1/2(xlog_e(x)-x) + C`

Explanation:

`log_e(sqrt(x))= 1/2log_e(x)` and

`d/(dx)(x log_e(x))=log_e(x) + 1`

then

`int log_e(sqrt(x))dx = 1/2 int log_e(x) dx= 1/2(xlog_e(x)-x) + C`