What is the integral of (175)/(e^{-x)+1} ?

The integral of (175)/(e^{-x)+1} is 175(ln|e^{-x}+1|+x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (175)/(e^{-x)+1}

\int \frac{175}{e ^{- x} + 1} d x

175 (ln e^{- x} + 1 + x) + C

Solution steps

\int \frac{175}{e ^{- x} + 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 175 \cdot \int \frac{1}{e ^{- x} + 1} d x

\frac{1}{e ^{- x} + 1} = - \frac{e ^{- x}}{e ^{- x} + 1} + 1

= 175 \cdot \int - \frac{e ^{- x}}{e ^{- x} + 1} + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 175 (- \int \frac{e ^{- x}}{e ^{- x} + 1} d x + \int 1 d x)

\int \frac{e ^{- x}}{e ^{- x} + 1} d x = - ln e^{- x} + 1

\int 1 d x = x

= 175 (- (- ln e^{- x} + 1) + x)

Simplify

= 175 (ln e^{- x} + 1 + x)

Add a constant to the solution

= 175 (ln e^{- x} + 1 + x) + C

\frac{d}{d x} (ln (7) x^{2})

f (x) = (3 x + 1) (x^{2} - 2)

\int \frac{4}{x ^{2} - 4 x + 13} d x

\int_{0}^{5} \frac{1}{x - 3} d x

θ \to 0 lim (\frac{θ}{sin ^{2} ( θ )})

What is the integral of (175)/(e^{-x)+1} ?
The integral of (175)/(e^{-x)+1} is 175(ln|e^{-x}+1|+x)+C