What is the integral of 5000e^{-0.04t} ?

The integral of 5000e^{-0.04t} is -125000e^{-0.04t}+C

Popular >

integral of 5000e^{-0.04t}

\int 5000 e^{- 0.04 t} d t

- 125000 e^{- 0.04 t} + C

Solution steps

\int 5000 e^{- 0.04 t} d t

Take the constant out:

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

= 5000 \cdot \int e^{- 0.04 t} d t

Apply u-substitution

: \int - \frac{1}{0.04} e^{u} d u

= 5000 \cdot \int - \frac{1}{0.04} e^{u} d u

Take the constant out:

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

= 5000 (- \frac{1}{0.04} \cdot \int e^{u} d u)

Simplify

= 5000 (- 25 \cdot \int e^{u} d u)

Use the common integral:

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

= 5000 (- 25 e^{u})

Substitute back

u = - 0.04 t

= 5000 (- 25 e^{- 0.04 t})

Simplify

= - 125000 e^{- 0.04 t}

Add a constant to the solution

= - 125000 e^{- 0.04 t} + C

\int \frac{4 sin ( x )}{1 + cos ^{2} ( x )} d x

\int \frac{ln ( 1 + tan ( x ) )}{cos ^{2} ( x )} d x

\int \frac{x}{( 9 + 4 x ^{2} ) ^{\frac{3}{2}}} d x

\int 1 + (x (x^{2} + 2)^{\frac{1}{2}})^{2} d x

\int (9 z^{2} + 14 z - 2) d z

What is the integral of 5000e^{-0.04t} ?
The integral of 5000e^{-0.04t} is -125000e^{-0.04t}+C