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

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

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integral from 1 to 3x of ln(x)

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

3 x ln (3 x) - 3 x + 1

Solution steps

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

Apply Integration By Parts

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

\int 1 d x = x

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

Compute the boundaries:

3 x ln (3 x) - 3 x + 1

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

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