What is the integral from 1 to 3 of ln(9x) ?

The integral from 1 to 3 of ln(9x) is 7ln(3)-2

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integral from 1 to 3 of ln(9x)

\int_{1}^{3} ln (9 x) d x

7 ln (3) - 2

Decimal

5.69028 \dots

Solution steps

\int_{1}^{3} ln (9 x) d x

Apply Integration By Parts

: [x ln (9 x) - \int 1 d x]_{1}^{3}

= [x ln (9 x) - \int 1 d x]_{1}^{3}

\int 1 d x = x

= [x ln (9 x) - x]_{1}^{3}

Compute the boundaries:

7 ln (3) - 2

= 7 ln (3) - 2

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

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

\int_{0}^{\frac{π}{2}} x cos^{3} (x) d x

What is the integral from 1 to 3 of ln(9x) ?
The integral from 1 to 3 of ln(9x) is 7ln(3)-2