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

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

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

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

2 e^{x} + 2 + C

Solution steps

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

Simplify

= \int \frac{e ^{x}}{e ^{x} + 2} 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} + 2

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 e^{x} + 2

Add a constant to the solution

= 2 e^{x} + 2 + C

\frac{\partial}{\partial y} (x^{4} - 2 y^{3})

\frac{d}{d x} (x - 2 arctan (x))

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

\frac{d}{d x} (sin (4 x + 1))

cos (t) + t sin (t), at t = 0

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