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

The integral of (e^x)/(8+e^x) is ln|8+e^x|+C

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integral of (e^x)/(8+e^x)

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

ln ∣ 8 + e^{x} ∣ + C

Solution steps

\int \frac{e ^{x}}{8 + e ^{x}} 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 = 8 + e^{x}

= ln ∣ 8 + e^{x} ∣

Add a constant to the solution

= ln ∣ 8 + e^{x} ∣ + C

y = (4 x - e^{3 x})^{9}

y = x^{2}, (0, 1)

\int (e^{y} + 1)^{2} e^{- y} d y

\int \frac{x ^{3}}{x ^{2} + x - 2} d x

\int \frac{x ^{4}}{x ^{5} - 2} d x

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