What is the integral of (15e^{5y})/(e^{5y)+2} ?

The integral of (15e^{5y})/(e^{5y)+2} is 3ln|e^{5y}+2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (15e^{5y})/(e^{5y)+2}

\int \frac{15 e ^{5 y}}{e ^{5 y} + 2} d y

3 ln e^{5 y} + 2 + C

Solution steps

\int \frac{15 e ^{5 y}}{e ^{5 y} + 2} d y

Take the constant out:

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

= 15 \cdot \int \frac{e ^{5 y}}{e ^{5 y} + 2} d y

Apply u-substitution

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

= 15 \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

= 15 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 15 \cdot \frac{1}{5} ln ∣ u ∣

Substitute back

u = e^{5 y} + 2

= 15 \cdot \frac{1}{5} ln e^{5 y} + 2

Simplify

15 \cdot \frac{1}{5} ln e^{5 y} + 2 : 3 ln e^{5 y} + 2

= 3 ln e^{5 y} + 2

Add a constant to the solution

= 3 ln e^{5 y} + 2 + C

x^{3} + y^{3} = 8 x y, (4, 4)

x \to 3 lim (1 0^{x^{2} - 3 \cdot x})

\frac{\partial}{\partial y} (x e^{9 x y})

x + 2, x^{2} - 4

\frac{\partial}{\partial x} (3 y^{2})

What is the integral of (15e^{5y})/(e^{5y)+2} ?
The integral of (15e^{5y})/(e^{5y)+2} is 3ln|e^{5y}+2|+C