What is the integral of 1/((\frac{1){e^x}+1)} ?

The integral of 1/((\frac{1){e^x}+1)} is ln|1+e^x|+C

Popular >

integral of 1/((\frac{1){e^x}+1)}

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

ln ∣ 1 + e^{x} ∣ + C

Solution steps

\int \frac{1}{\frac{1}{e ^{x}} + 1} d x

Simplify

\frac{1}{\frac{1}{e ^{x}} + 1} : \frac{e ^{x}}{1 + e ^{x}}

= \int \frac{e ^{x}}{1 + 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 = 1 + e^{x}

= ln ∣ 1 + e^{x} ∣

Add a constant to the solution

= ln ∣ 1 + e^{x} ∣ + C

y = x^{2} - 5 x, (5, 0)

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

3 x^{6} - 6 x^{6} y^{7} + 4 x^{5} y^{4}

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

\int_{1}^{3} 5 x e^{x} d x

What is the integral of 1/((\frac{1){e^x}+1)} ?
The integral of 1/((\frac{1){e^x}+1)} is ln|1+e^x|+C