What is the integral of (ln(t))/t ?

The integral of (ln(t))/t is (ln^2(t))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (ln(t))/t

\int \frac{ln ( t )}{t} d t

\frac{ln ^{2} ( t )}{2} + C

Solution steps

\int \frac{ln ( t )}{t} d t

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = ln (t)

= \frac{ln ^{2} ( t )}{2}

Add a constant to the solution

= \frac{ln ^{2} ( t )}{2} + C

\frac{d}{d x} ((1 + e^{x})^{- 2})

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\int_{0}^{1} \frac{x}{4 - x ^{2}} d x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 5 y = 0

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