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

The integral from 1 to 3 of ln(x^3) is 9ln(3)-6

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integral from 1 to 3 of ln(x^3)

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

9 ln (3) - 6

Decimal

3.88751 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int 3 d x = 3 x

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

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

Compute the boundaries:

9 ln (3) - 6

= 9 ln (3) - 6

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What is the integral from 1 to 3 of ln(x^3) ?
The integral from 1 to 3 of ln(x^3) is 9ln(3)-6