What is the integral of e^{ln|t|} ?

The integral of e^{ln|t|} is (t|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 e^{ln|t|}

\int e^{l n ∣ t ∣} d t

\frac{t ∣ t ∣}{2} + C

Solution steps

\int e^{l n ∣ t ∣} d t

Apply log rule:

a^{l o g_{a} (b)} = b

= \int ∣ t ∣ d t

Use the common integral:

\int ∣ t ∣ d t = \frac{t ∣ t ∣}{2}

= \frac{t ∣ t ∣}{2}

Add a constant to the solution

= \frac{t ∣ t ∣}{2} + C

\int \frac{1}{S} d S

f (x) = \frac{( x - 4 )}{x - 2}

\frac{d}{d x} (cos (x) + x)

\int \frac{3}{4} x^{\frac{1}{2}} d x

\int_{1}^{8} (\frac{x ^{- \frac{1}{2}}}{1 + x ^{\frac{1}{2}}}) d x