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

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

Popular >

integral of-3e^{-3x}

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

e^{- 3 x} + C

Solution steps

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

Apply u-substitution

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

= - 3 \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

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

Use the common integral:

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

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

Substitute back

u = - 3 x

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

Simplify

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

= e^{- 3 x}

Add a constant to the solution

= e^{- 3 x} + C

\frac{d}{d x} (7 sin (x) + 7 x cos (x))

\int - 3 y^{2} d y

\int \frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}} d t

\frac{\partial}{\partial x} ((x - 1)^{2})

\frac{d}{d x} (3^{- x^{2}})