What is the integral of 3e^{-0.2x} ?

The integral of 3e^{-0.2x} is -15e^{-0.2x}+C

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integral of 3e^{-0.2x}

\int 3 e^{- 0.2 x} d x

- 15 e^{- 0.2 x} + C

Solution steps

\int 3 e^{- 0.2 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^{- 0.2 x} d x

Apply u-substitution

: \int - \frac{1}{0.2} e^{u} d u

= 3 \cdot \int - \frac{1}{0.2} 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}{0.2} \cdot \int e^{u} d u)

Simplify

= 3 (- 5 \cdot \int e^{u} d u)

Use the common integral:

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

= 3 (- 5 e^{u})

Substitute back

u = - 0.2 x

= 3 (- 5 e^{- 0.2 x})

Simplify

= - 15 e^{- 0.2 x}

Add a constant to the solution

= - 15 e^{- 0.2 x} + C

y^{^{'}} = \frac{( x + 3 y )}{( y - 3 x )}

sec (5 x)

f (x) = 5 x^{2} + 5 x + 7

\frac{\partial}{\partial x} (arctan (\frac{y}{( x - 1 )}))

What is the integral of 3e^{-0.2x} ?
The integral of 3e^{-0.2x} is -15e^{-0.2x}+C