What is the integral of 3e^{2x} ?

The integral of 3e^{2x} is 3/2 e^{2x}+C

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integral of 3e^{2x}

\int 3 e^{2 x} d x

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

Solution steps

\int 3 e^{2 x} d x

Take the constant out:

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

= 3 \cdot \int e^{2 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{2} d u

= 3 \cdot \int e^{u} \frac{1}{2} d u

Take the constant out:

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

= 3 \cdot \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= 3 \cdot \frac{1}{2} e^{u}

Substitute back

u = 2 x

= 3 \cdot \frac{1}{2} e^{2 x}

Simplify

3 \cdot \frac{1}{2} e^{2 x} : \frac{3}{2} e^{2 x}

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (x^{2} y + x y^{3})

\frac{\partial}{\partial x} (cos (x) cos (y))

\frac{d x}{d t} = \frac{457.8 - 7 x}{2180}

(1 - e^{x^{3}})^{5}

x \to 1 - lim (x^{2} - 2)