What is the integral of (5e^x)/(e^x+4) ?

The integral of (5e^x)/(e^x+4) is 5ln|e^x+4|+C

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integral of (5e^x)/(e^x+4)

\int \frac{5 e ^{x}}{e ^{x} + 4} d x

5 ln ∣ e^{x} + 4 ∣ + C

Solution steps

\int \frac{5 e ^{x}}{e ^{x} + 4} d x

Take the constant out:

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

= 5 \cdot \int \frac{e ^{x}}{e ^{x} + 4} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 ln ∣ u ∣

Substitute back

u = e^{x} + 4

= 5 ln ∣ e^{x} + 4 ∣

Add a constant to the solution

= 5 ln ∣ e^{x} + 4 ∣ + C

x \to 8 - lim (\frac{6 x}{x - 8})

f (t) = t^{2} + 1

\frac{\partial}{\partial t} (s^{2} t)

n = 2 \sum \infty e^{3 - 6 n}

\frac{d}{d x} (\frac{3}{2 x + 7})

What is the integral of (5e^x)/(e^x+4) ?
The integral of (5e^x)/(e^x+4) is 5ln|e^x+4|+C