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

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

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

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

2 e^{x + 1} + C

Solution steps

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

Apply u-substitution

: \int 2 e^{u} d u

= \int 2 e^{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= 2 e^{u}

Substitute back

u = x + 1

= 2 e^{x + 1}

Add a constant to the solution

= 2 e^{x + 1} + C

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