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

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

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

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

2 e^{x + 3} + C

Solution steps

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

= 2 e^{x + 3}

Add a constant to the solution

= 2 e^{x + 3} + C

y = - \frac{1}{2} x^{2} + 2, y = 0

(y^{2} + 1) d x = y sec^{2} (x) d y

x \to 0 lim (x^{- 2})

(2 x) d x + (2 y - 4 x^{2} y^{- 1}) d y = 0

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