What is the integral from 0 to 1 of (ln(t))/t ?

The integral from 0 to 1 of (ln(t))/t is diverges

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integral from 0 to 1 of (ln(t))/t

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

diverges

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{1 - ln ( t )}{t} d t = - \frac{( 1 - ln ( t ) ) ^{2}}{2}

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

Simplify

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

= [\frac{1}{2} (ln^{2} (t) + 1)]_{0}^{1}

Compute the boundaries:

diverges

= diverges

\int + x^{3} e^{3 x^{2}} d x

x \to 1 + lim (\frac{x ^{2} - 4}{x - 1})

\int \frac{20000}{( x + 100 ) ^{3}} d x

\int 8 x e^{x^{2}} d x

\int (- 1) d x

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