What is the integral of log_{e}(5x) ?

The integral of log_{e}(5x) is xln(5x)-x+C

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integral of log_{e}(5x)

\int lo g_{e} (5 x) d x

x ln (5 x) - x + C

Solution steps

\int lo g_{e} (5 x) d x

Apply log rule:

lo g_{e} (x) = ln (x)

= \int ln (5 x) d x

Apply Integration By Parts

: x ln (5 x) - \int 1 d x

= x ln (5 x) - \int 1 d x

\int 1 d x = x

= x ln (5 x) - x

Add a constant to the solution

= x ln (5 x) - x + C

f (x) = - 2 sin (x)

300 - 3 p

\frac{\partial}{\partial x} (arcsin (y))

\int \frac{x}{1 + cos ( 2 x )} d x

arcsin (3 x)

What is the integral of log_{e}(5x) ?
The integral of log_{e}(5x) is xln(5x)-x+C