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

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

Popular >

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

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

diverges

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{2}{x ^{2}} d x = \frac{2}{x}

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

Simplify

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

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

Compute the boundaries:

diverges

= diverges

\int_{0}^{2} 3 - \frac{4 e ^{0.28 t}}{e ^{0.28 t} + 10.13} d t

\int_{0}^{π} e^{- in x} d x

\int_{0}^{\frac{π}{4}} 5 e^{s i n (x)} cos (x) d x

\int_{0}^{2} k (4 x - 2 x^{2}) d x

\int_{0}^{3} \frac{4 x ( 9 - x ^{2} )}{81} d x

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