What is the integral from 1 to e of ln(3x) ?

The integral from 1 to e of ln(3x) is eln(3e)-e-ln(3)+1

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integral from 1 to e of ln(3x)

\int_{1}^{e} ln (3 x) d x

e ln (3 e) - e - ln (3) + 1

Decimal Notation

2.88772 \dots

Solution steps

\int_{1}^{e} ln (3 x) d x

Apply Integration By Parts

: [x ln (3 x) - \int 1 d x]_{1}^{e}

= [x ln (3 x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= [x ln (3 x) - x]_{1}^{e}

Compute the boundaries:

e ln (3 e) - e - ln (3) + 1

= e ln (3 e) - e - ln (3) + 1

\frac{d}{d x} (tan^{3} (x) + tan (x^{3}))

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

\frac{d y}{d x} - 2 x y = x

\frac{d y}{d x} + y - cos (x) = 0

f (x) = x^{3} (x - 1)^{2}

What is the integral from 1 to e of ln(3x) ?
The integral from 1 to e of ln(3x) is eln(3e)-e-ln(3)+1