What is the integral of 1/(sqrt(x+4))e^{sqrt(x+4)} ?

The integral of 1/(sqrt(x+4))e^{sqrt(x+4)} is 2e^{sqrt(x+4)}+C

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integral of 1/(sqrt(x+4))e^{sqrt(x+4)}

\int \frac{1}{x + 4} e^{x + 4} d x

2 e^{x + 4} + C

Solution steps

\int \frac{1}{x + 4} e^{x + 4} d x

Simplify

\frac{1}{x + 4} e^{x + 4} : \frac{e ^{x + 4}}{x + 4}

= \int \frac{e ^{x + 4}}{x + 4} 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 + 4

= 2 e^{x + 4}

Add a constant to the solution

= 2 e^{x + 4} + C

\int arctan (\frac{y}{x}) d x

\int \frac{ln ( x ^{2} )}{x ^{4}} d x

\int \frac{( x ^{3} + 1 )}{x ^{4} + 4 x} d x

2

\int 3^{u} d u

What is the integral of 1/(sqrt(x+4))e^{sqrt(x+4)} ?
The integral of 1/(sqrt(x+4))e^{sqrt(x+4)} is 2e^{sqrt(x+4)}+C