What is the integral of 2ln(3x) ?

The integral of 2ln(3x) is 2(xln(3x)-x)+C

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integral of 2ln(3x)

\int 2 ln (3 x) d x

2 (x ln (3 x) - x) + C

Solution steps

\int 2 ln (3 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int ln (3 x) d x

Apply Integration By Parts

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

= 2 (x ln (3 x) - \int 1 d x)

\int 1 d x = x

= 2 (x ln (3 x) - x)

Add a constant to the solution

= 2 (x ln (3 x) - x) + C

csc (5 x) cot (5 x)

\frac{7}{x}

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

\frac{d}{d x} (x ln (a))

\frac{d}{d x} (22 (2 e^{x^{2}} x^{2} + e^{x^{2}}))