What is the integral of (e^x)/(sqrt(e^x+1)) ?

The integral of (e^x)/(sqrt(e^x+1)) is 2sqrt(e^x+1)+C

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integral of (e^x)/(sqrt(e^x+1))

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

2 e^{x} + 1 + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = e^{x} + 1

= 2 (e^{x} + 1)^{\frac{1}{2}}

Apply radical rule:

= 2 e^{x} + 1

Add a constant to the solution

= 2 e^{x} + 1 + C

\frac{d}{d x} (0.02 e^{x} x^{3})

x (x^{2} + 4)

\frac{( x ^{2} - 1 )}{x ^{2} + 1}

f (x) = \frac{e ^{x} - e ^{x}}{e ^{x} + e ^{x}}

x \to - 2 lim (x^{2} - 3 x + 4)

What is the integral of (e^x)/(sqrt(e^x+1)) ?
The integral of (e^x)/(sqrt(e^x+1)) is 2sqrt(e^x+1)+C