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

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

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integral of (e^t)/(e^t+4)

\int \frac{e ^{t}}{e ^{t} + 4} d t

ln e^{t} + 4 + C

Solution steps

\int \frac{e ^{t}}{e ^{t} + 4} d t

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^{t} + 4

= ln e^{t} + 4

Add a constant to the solution

= ln e^{t} + 4 + C

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

\int \frac{1}{( x ^{2} + 4 ) ^{3}} d x

\int \frac{1}{( x ^{3} - 1 ) ^{2}} d x

\int \frac{6 x + 2}{( x + 1 ) ( 2 x + 1 )} d x

\int 2 e^{x} 1 - e^{2 x} d x

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