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

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

\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

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

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

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

\int_{1}^{3} 3 x (x - 4) d x

im pl i c i t \frac{d y}{d x}, e^{4 x} = sin (x + 5 y)

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