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

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

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

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

2 1 + e^{x} + C

Solution steps

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

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

Apply radical rule:

= 2 1 + e^{x}

Add a constant to the solution

= 2 1 + e^{x} + C

\int x^{9} x^{5} + 3 d x

\frac{d}{d x} (ln ((5 x)^{2}))

y^{^{''}} + 7 y^{^{'}} = 0

\frac{d}{d x} (cot (3 - 2 x))

\frac{d ^{2} y}{d t ^{2}} + 5 \frac{d y}{d t} + 6 y = 1

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