What is the integral from 3 to 4 of ln(x^2) ?

The integral from 3 to 4 of ln(x^2) is 16ln(2)-2-6ln(3)

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integral from 3 to 4 of ln(x^2)

\int_{3}^{4} ln (x^{2}) d x

16 ln (2) - 2 - 6 ln (3)

Decimal

2.49868 \dots

Solution steps

\int_{3}^{4} ln (x^{2}) d x

Apply Integration By Parts

= [x ln (x^{2}) - \int 2 d x]_{3}^{4}

\int 2 d x = 2 x

= [x ln (x^{2}) - 2 x]_{3}^{4}

Apply log rule

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

assuming

x \geq 0

= [2 x ln (x) - 2 x]_{3}^{4}

Compute the boundaries:

16 ln (2) - 2 - 6 ln (3)

= 16 ln (2) - 2 - 6 ln (3)

What is the integral from 3 to 4 of ln(x^2) ?
The integral from 3 to 4 of ln(x^2) is 16ln(2)-2-6ln(3)