What is the integral of log_{e}(2x) ?

The integral of log_{e}(2x) is xln(2x)-x+C

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integral of log_{e}(2x)

\int lo g_{e} (2 x) d x

x ln (2 x) - x + C

Solution steps

\int lo g_{e} (2 x) d x

Apply Integration By Parts

: x ln (2 x) - \int 1 d x

= x ln (2 x) - \int 1 d x

\int 1 d x = x

= x ln (2 x) - x

Add a constant to the solution

= x ln (2 x) - x + C

(x - 1)^{\frac{2}{3}}

\frac{\partial}{\partial x} (\frac{x}{y} - \frac{y}{z})

\frac{d}{d x} (81 sin (3 x))

\int 2 x^{2} - 3 x + 5 d x

\frac{d y}{d t} + \frac{23 y}{t} = \frac{1}{t}

What is the integral of log_{e}(2x) ?
The integral of log_{e}(2x) is xln(2x)-x+C