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

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

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integral from-1 to 2 of (ln(x^2))/x

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

diverges

Solution steps

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

Find undefined (singularity) points:

x = 0

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 1}^{0} \frac{ln ( x ^{2} )}{x} d x + \int_{0}^{2} \frac{ln ( x ^{2} )}{x} d x

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

\int_{0}^{4} x x + 1 d x

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\int_{0}^{2} x^{3} - 4 x^{2} + 3 x d x

\int_{1}^{\infty} \frac{1}{1 0 ^{x}} d x

\int_{0}^{1} (35 - 10 x) d x

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