What is the integral of 12e^{6x} ?

The integral of 12e^{6x} is 2e^{6x}+C

Popular >

integral of 12e^{6x}

\int 12 e^{6 x} d x

2 e^{6 x} + C

Solution steps

\int 12 e^{6 x} d x

Take the constant out:

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

= 12 \cdot \int e^{6 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{6} d u

= 12 \cdot \int e^{u} \frac{1}{6} d u

Take the constant out:

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

= 12 \cdot \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= 12 \cdot \frac{1}{6} e^{u}

Substitute back

u = 6 x

= 12 \cdot \frac{1}{6} e^{6 x}

Simplify

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

= 2 e^{6 x}

Add a constant to the solution

= 2 e^{6 x} + C

\frac{1}{3 + 2 x}

\int (x^{4} + x^{2})^{8} (4 x^{3} + 2 x) d x

y^{^{''}} + 4 y = sin (2 x) cos (2 x)

\frac{d}{d x} (21 \cdot π \cdot x^{2})

y = ln (3 x^{2} + 7 y^{2})