What is the integral of (e^{8x})/(e^{8x)+4} ?

The integral of (e^{8x})/(e^{8x)+4} is 1/8 ln|e^{8x}+4|+C

Popular >

integral of (e^{8x})/(e^{8x)+4}

\int \frac{e ^{8 x}}{e ^{8 x} + 4} d x

\frac{1}{8} ln e^{8 x} + 4 + C

Solution steps

\int \frac{e ^{8 x}}{e ^{8 x} + 4} d x

Apply u-substitution

: \int \frac{1}{8 u} d u

= \int \frac{1}{8 u} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{8} ln ∣ u ∣

Substitute back

u = e^{8 x} + 4

= \frac{1}{8} ln e^{8 x} + 4

Add a constant to the solution

= \frac{1}{8} ln e^{8 x} + 4 + C

f (x) = x^{2} + 3 x - 1, at x = 0

x \to 0 - lim (x \cdot ln (x))

\frac{d}{d x} (\frac{6 x + y}{x ^{2} + y ^{2}})

x \to 3 lim (\frac{x - 3}{x ^{2} - 3})

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

What is the integral of (e^{8x})/(e^{8x)+4} ?
The integral of (e^{8x})/(e^{8x)+4} is 1/8 ln|e^{8x}+4|+C