What is the integral from 0 to 2 of ln(x^3) ?

The integral from 0 to 2 of ln(x^3) is 6ln(2)-6

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integral from 0 to 2 of ln(x^3)

\int_{0}^{2} ln (x^{3}) d x

6 ln (2) - 6

Decimal Notation

- 1.84111 \dots

Solution steps

\int_{0}^{2} ln (x^{3}) d x

Apply Integration By Parts

: [x ln (x^{3}) - \int 3 d x]_{0}^{2}

= [x ln (x^{3}) - \int 3 d x]_{0}^{2}

\int 3 d x = 3 x

= [x ln (x^{3}) - 3 x]_{0}^{2}

Apply log rule

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

assuming

x \geq 0

= [3 x ln (x) - 3 x]_{0}^{2}

Compute the boundaries:

6 ln (2) - 6

= 6 ln (2) - 6

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\int_{1}^{2} ∣ 2 x - 3 ∣ d x

What is the integral from 0 to 2 of ln(x^3) ?
The integral from 0 to 2 of ln(x^3) is 6ln(2)-6