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

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

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integral of e^{sqrt(4x)}

\int e^{4 x} d x

e^{2 x} x - \frac{1}{2} e^{2 x} + C

Solution steps

\int e^{4 x} d x

Apply Integration By Parts

: e^{2 x} x - \int e^{2 x} x d x

= e^{2 x} x - \int e^{2 x} x d x

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

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

Simplify

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

= e^{2 x} x - \frac{1}{2} e^{2 x}

Add a constant to the solution

= e^{2 x} x - \frac{1}{2} e^{2 x} + C

\int (csc (5 x))^{3} d x

f (x) = ln (x + 2)

\frac{d}{d x} (sin (\frac{5 x - 3 x ^{3}}{x + 1}))

x^{n}

\int \frac{3 x ^{2} + x + 1}{x ^{2} - 2 x + 5} d x

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