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

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

Popular >

integral of e^{sqrt(3x)}

\int e^{3 x} d x

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

Solution steps

\int e^{3 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}{3} (3 e^{3 x} x - 2 (3 e^{3 x} x - e^{3 x}))

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

Simplify

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

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

Add a constant to the solution

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

8 x^{2} + 3 x

\frac{d}{d x} (2 c x + c^{2})

f (x) = 2 x^{2} - x^{3}

(2 t - 1) (4 t - 6)^{- 1}

x^{2} y^{^{''}} - 2 y = 0, y (1) = 0, y^{^{'}} (1) = 3

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