What is the integral of (e^x)/(e^x+6) ?

The integral of (e^x)/(e^x+6) is ln|e^x+6|+C

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integral of (e^x)/(e^x+6)

\int \frac{e ^{x}}{e ^{x} + 6} d x

ln ∣ e^{x} + 6 ∣ + C

Solution steps

\int \frac{e ^{x}}{e ^{x} + 6} 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} + 6

= ln ∣ e^{x} + 6 ∣

Add a constant to the solution

= ln ∣ e^{x} + 6 ∣ + C

x e^{- \frac{1}{x}}

x (e^{\frac{y}{x}} - 1) \frac{d y}{d x} = e^{\frac{y}{x}} (y - x)

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{3}})

\int \frac{sin ( x )}{cos ( x ) - cos ^{2} ( x )} d x

\frac{d y}{d x} = \frac{( 1 - y )}{1 - x}

What is the integral of (e^x)/(e^x+6) ?
The integral of (e^x)/(e^x+6) is ln|e^x+6|+C