What is the integral of 18e^{-3x} ?

The integral of 18e^{-3x} is -6e^{-3x}+C

Popular >

integral of 18e^{-3x}

\int 18 e^{- 3 x} d x

- 6 e^{- 3 x} + C

Solution steps

\int 18 e^{- 3 x} d x

Take the constant out:

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

= 18 \cdot \int e^{- 3 x} d x

Apply u-substitution

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

= 18 \cdot \int - \frac{1}{3} e^{u} d u

Take the constant out:

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

= 18 (- \frac{1}{3} \cdot \int e^{u} d u)

Use the common integral:

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

= 18 (- \frac{1}{3} e^{u})

Substitute back

u = - 3 x

= 18 (- \frac{1}{3} e^{- 3 x})

Simplify

18 (- \frac{1}{3} e^{- 3 x}) : - 6 e^{- 3 x}

= - 6 e^{- 3 x}

Add a constant to the solution

= - 6 e^{- 3 x} + C

\int \frac{1}{x ^{2} + m} d x

\int 5 t d t

\int \frac{sin ( x )}{4 + cos ^{2} ( x )} d x

\int y ln (x) + x ln (y) + z^{2} d z

\int sin (32 x) sin (cos (32 x)) d x