What is the integral from 0 to 1 of ln(9x) ?

The integral from 0 to 1 of ln(9x) is 2ln(3)-1

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integral from 0 to 1 of ln(9x)

\int_{0}^{1} ln (9 x) d x

2 ln (3) - 1

Decimal

1.19722 \dots

Solution steps

\int_{0}^{1} ln (9 x) d x

Apply Integration By Parts

: [x ln (9 x) - \int 1 d x]_{0}^{1}

= [x ln (9 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= [x ln (9 x) - x]_{0}^{1}

Compute the boundaries:

2 ln (3) - 1

= 2 ln (3) - 1

\int 7 x + 2 d x

\int (z - z)^{2} d z

\int \frac{x}{16 - x ^{2}} d x

6 x^{4} ln (x)

x \to 2 - lim (x)

What is the integral from 0 to 1 of ln(9x) ?
The integral from 0 to 1 of ln(9x) is 2ln(3)-1