What is the integral of e^{sqrt(9x)} ?

The integral of e^{sqrt(9x)} is 2/3 e^{3sqrt(x)}sqrt(x)-2/9 e^{3sqrt(x)}+C

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integral of e^{sqrt(9x)}

\int e^{9 x} d x

\frac{2}{3} e^{3 x} x - \frac{2}{9} e^{3 x} + C

Solution steps

\int e^{9 x} d x

Apply Integration By Parts

: e^{3 x} x - \int \frac{3}{2} e^{3 x} x d x

= e^{3 x} x - \int \frac{3}{2} e^{3 x} x d x

\int \frac{3}{2} e^{3 x} x d x = \frac{1}{9} e^{3 x} (9 x - 6 x + 2)

= e^{3 x} x - \frac{1}{9} e^{3 x} (9 x - 6 x + 2)

Simplify

e^{3 x} x - \frac{1}{9} e^{3 x} (9 x - 6 x + 2) : \frac{2}{3} e^{3 x} x - \frac{2}{9} e^{3 x}

= \frac{2}{3} e^{3 x} x - \frac{2}{9} e^{3 x}

Add a constant to the solution

= \frac{2}{3} e^{3 x} x - \frac{2}{9} e^{3 x} + C

x \to 2 lim (x + 6)

\frac{d}{d t} (x ln (t))

y = x^{3} - x, y = 3 x, - 2, 2

\frac{d}{d x} ((1 + 3 x^{2}) (x - x^{2}))

\frac{d}{d x} (\frac{- 4 x + 1 + x}{x ^{2} - 1})

What is the integral of e^{sqrt(9x)} ?
The integral of e^{sqrt(9x)} is 2/3 e^{3sqrt(x)}sqrt(x)-2/9 e^{3sqrt(x)}+C