What is the integral of (5e^{5t})/(7+e^{5t)} ?

The integral of (5e^{5t})/(7+e^{5t)} is ln|7+e^{5t}|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5e^{5t})/(7+e^{5t)}

\int \frac{5 e ^{5 t}}{7 + e ^{5 t}} d t

ln 7 + e^{5 t} + C

Solution steps

\int \frac{5 e ^{5 t}}{7 + e ^{5 t}} d t

Take the constant out:

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

= 5 \cdot \int \frac{e ^{5 t}}{7 + e ^{5 t}} d t

Apply u-substitution

: \int \frac{1}{5 u} d u

= 5 \cdot \int \frac{1}{5 u} d u

Take the constant out:

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

= 5 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 \cdot \frac{1}{5} ln ∣ u ∣

Substitute back

u = 7 + e^{5 t}

= 5 \cdot \frac{1}{5} ln 7 + e^{5 t}

Simplify

5 \cdot \frac{1}{5} ln 7 + e^{5 t} : ln 7 + e^{5 t}

= ln 7 + e^{5 t}

Add a constant to the solution

= ln 7 + e^{5 t} + C

\frac{\partial}{\partial x} (3 x + 2 y sin (x))

\frac{d}{d x} (6^{x} lo g_{3} (x))

y = (6 x^{2} - 10 x + 1)^{- 4}

\int [\frac{( sin ( x ) )}{x}] d x

\frac{d}{d x} (3 + 4.1 cos (0.9 x))

What is the integral of (5e^{5t})/(7+e^{5t)} ?
The integral of (5e^{5t})/(7+e^{5t)} is ln|7+e^{5t}|+C