What is the integral of (ln(3x)) ?

The integral of (ln(3x)) is xln(3x)-x+C

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integral of (ln(3x))

\int (ln (3 x)) d x

x ln (3 x) - x + C

Solution steps

\int ln (3 x) d x

Apply Integration By Parts

: x ln (3 x) - \int 1 d x

= x ln (3 x) - \int 1 d x

\int 1 d x = x

= x ln (3 x) - x

Add a constant to the solution

= x ln (3 x) - x + C

\frac{\partial}{\partial y} (x y - 5 y + x^{2} + y^{2} - 10 x)

f (x) = \frac{1}{x ^{3}}

\int 1 - 3 x d x

\int_{0}^{1} e^{- x^{2}} d x

x y \frac{d y}{d x} + y^{2} = 2 x