What is the integral of (e^x)/(e^x+7) ?

The integral of (e^x)/(e^x+7) is ln|e^x+7|+C

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integral of (e^x)/(e^x+7)

\int \frac{e ^{x}}{e ^{x} + 7} d x

ln ∣ e^{x} + 7 ∣ + C

Solution steps

\int \frac{e ^{x}}{e ^{x} + 7} 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} + 7

= ln ∣ e^{x} + 7 ∣

Add a constant to the solution

= ln ∣ e^{x} + 7 ∣ + C

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

\int (x + 7) (x - 6) d x

\int sin (3 x) + cos (2 x) d x

\int (2 x^{2} - 5)^{2} d x

\int \frac{x - 2}{( x - 1 ) ^{2}} d x

What is the integral of (e^x)/(e^x+7) ?
The integral of (e^x)/(e^x+7) is ln|e^x+7|+C