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

The integral from 0 to 2 of ln(x^2) is 4ln(2)-4

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

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

4 ln (2) - 4

Decimal Notation

- 1.22741 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int 2 d x = 2 x

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

Apply log rule

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

assuming

x \geq 0

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

Compute the boundaries:

4 ln (2) - 4

= 4 ln (2) - 4

\frac{\partial}{\partial x} (\frac{1}{2} (a + b) h)

sin (0)

f (t) = e^{e^{e^{e^{t}}}}

\frac{d}{d t} (4 ln (t))

\int \frac{3 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}} d x

What is the integral from 0 to 2 of ln(x^2) ?
The integral from 0 to 2 of ln(x^2) is 4ln(2)-4