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

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

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

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

0

Solution steps

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

Apply Integration By Parts

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

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

\int 2 d x = 2 x

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

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}^{e}

Compute the boundaries:

0

= 0

\int_{- 1}^{1} (3 x - 2) d x

y = \frac{3}{x}

\int sin^{2} (x) cos^{2} (2 x) d x

\frac{d}{d x} (f (x) x)

x \to - 3 + lim (\frac{∣ x + 3 ∣}{x + 3})

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