What is the integral of (e^x)/(sqrt(e^x+3)) ?

The integral of (e^x)/(sqrt(e^x+3)) is 2sqrt(e^x+3)+C

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integral of (e^x)/(sqrt(e^x+3))

\int \frac{e ^{x}}{e ^{x} + 3} d x

2 e^{x} + 3 + C

Solution steps

\int \frac{e ^{x}}{e ^{x} + 3} 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} + 3

= 2 (e^{x} + 3)^{\frac{1}{2}}

Apply radical rule:

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

= 2 e^{x} + 3

Add a constant to the solution

= 2 e^{x} + 3 + C

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What is the integral of (e^x)/(sqrt(e^x+3)) ?
The integral of (e^x)/(sqrt(e^x+3)) is 2sqrt(e^x+3)+C