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

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

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

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

ln ∣ e^{x} + 5 ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = e^{x} + 5

= ln ∣ e^{x} + 5 ∣

Add a constant to the solution

= ln ∣ e^{x} + 5 ∣ + C

f (x) = arccot (x)

\int x^{13} cos (x^{7}) d x

\frac{d}{d x} (\frac{x ^{2} - 4 x + 3}{2 x ^{2} - 3 x + 2})

\frac{\partial}{\partial y} (2 x^{2} - x^{4} + y^{2})

\frac{\partial}{\partial x} (2 x^{2} + y^{2} + 2 x y + y x + 7 y)

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