What is the integral of 12e^{3x} ?

The integral of 12e^{3x} is 4e^{3x}+C

Popular >

integral of 12e^{3x}

\int 12 e^{3 x} d x

4 e^{3 x} + C

Solution steps

\int 12 e^{3 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^{3 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{3} d u

= 12 \cdot \int e^{u} \frac{1}{3} d u

Take the constant out:

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

= 12 \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= 12 \cdot \frac{1}{3} e^{u}

Substitute back

u = 3 x

= 12 \cdot \frac{1}{3} e^{3 x}

Simplify

12 \cdot \frac{1}{3} e^{3 x} : 4 e^{3 x}

= 4 e^{3 x}

Add a constant to the solution

= 4 e^{3 x} + C

\int (1 - t) (2 + t^{2}) d t

\frac{d ^{2}}{d x ^{2}} (cot (2 x) + 3 x^{2})

\frac{d}{d x} (lo g_{2} (2 x))

\frac{d}{d x} (arccot (\frac{x}{2}))

f (x) = 7 - x^{2}