What is the integral of 6e^{2x} ?

The integral of 6e^{2x} is 3e^{2x}+C

Popular >

integral of 6e^{2x}

\int 6 e^{2 x} d x

3 e^{2 x} + C

Solution steps

\int 6 e^{2 x} d x

Take the constant out:

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

= 6 \cdot \int e^{2 x} d x

Apply u-substitution

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

= 6 \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

= 6 \cdot \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= 6 \cdot \frac{1}{2} e^{u}

Substitute back

u = 2 x

= 6 \cdot \frac{1}{2} e^{2 x}

Simplify

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

= 3 e^{2 x}

Add a constant to the solution

= 3 e^{2 x} + C

4 cos (t) - 9 sin (t)

\frac{\partial}{\partial x} (x^{9} y z^{2} + 5 yz)

\int cos^{3} (2 x) sin^{3} (2 x) d x

cos (y) y^{^{'}} = e^{2 x} + 1

\frac{y ^{3}}{30} + \frac{5}{2 y}