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

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

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integral of e^{3sqrt(x)}

\int e^{3 x} d x

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

Solution steps

\int e^{3 x} d x

Apply u-substitution

: \int \frac{2 e ^{u} u}{9} d u

= \int \frac{2 e ^{u} u}{9} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{9} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= \frac{2}{9} (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= \frac{2}{9} (e^{u} u - e^{u})

Substitute back

u = 3 x

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

Add a constant to the solution

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

x^{- 1}

\int \frac{1}{x} \frac{1 - x}{1 + x} d x

\int 9 x^{2} arcsin (x) d x

\int \frac{arcsin ( e ^{x} )}{e ^{x}} d x

\int \frac{cos ( t )}{sin ( t ) + cos ( t )} d t

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