What is the integral from 0 to 1 of ln(x^2) ?

The integral from 0 to 1 of ln(x^2) is -2

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integral from 0 to 1 of ln(x^2)

\int_{0}^{1} ln (x^{2}) d x

- 2

Solution steps

\int_{0}^{1} ln (x^{2}) d x

Apply Integration By Parts

: [x ln (x^{2}) - \int 2 d x]_{0}^{1}

= [x ln (x^{2}) - \int 2 d x]_{0}^{1}

\int 2 d x = 2 x

= [x ln (x^{2}) - 2 x]_{0}^{1}

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}^{1}

Compute the boundaries:

- 2

= - 2

\int_{0}^{3} \frac{x}{x ^{2} + 7} d x

\int_{0}^{1} \frac{1}{x ^{2} - 25} d x

\int_{4}^{7} x e^{7 x} d x

\int_{0}^{3} 3 t - 5 d t

\int_{0}^{1} 2 x - 1 d x

What is the integral from 0 to 1 of ln(x^2) ?
The integral from 0 to 1 of ln(x^2) is -2