What is the integral from 0 to 1 of ln(3x) ?

The integral from 0 to 1 of ln(3x) is ln(3)-1

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integral from 0 to 1 of ln(3x)

\int_{0}^{1} ln (3 x) d x

ln (3) - 1

Decimal Notation

0.09861 \dots

Solution steps

\int_{0}^{1} ln (3 x) d x

Apply Integration By Parts

: [x ln (3 x) - \int 1 d x]_{0}^{1}

= [x ln (3 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= [x ln (3 x) - x]_{0}^{1}

Compute the boundaries:

ln (3) - 1

= ln (3) - 1

\int \frac{2 x}{( 2 + 3 x ^{2} ) ^{3}} d x

\int_{0}^{4} \frac{1}{x ^{2} + 16} d x

\frac{x}{4 + x}

\frac{\partial}{\partial x} (x y + x e^{\frac{y}{x}})

\int 8 t e^{t} d t

What is the integral from 0 to 1 of ln(3x) ?
The integral from 0 to 1 of ln(3x) is ln(3)-1