What is the integral of ge^{-ct} ?

The integral of ge^{-ct} is -ge^{-ct} 1/c+C

Popular >

integral of ge^{-ct}

\int g e^{- c t} d t

- g e^{- c t} \frac{1}{c} + C

Solution steps

\int g e^{- c t} d t

Take the constant out:

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

= g \cdot \int e^{- c t} d t

Apply u-substitution

: \int - \frac{e ^{u}}{c} d u

= g \cdot \int - \frac{e ^{u}}{c} d u

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = - c t

= g (- \frac{1}{c} e^{- c t})

Simplify

= - g e^{- c t} \frac{1}{c}

Add a constant to the solution

= - g e^{- c t} \frac{1}{c} + C

\frac{d}{d x} (a x sin (4 x) + b x cos (4 x))

f^{^{'}} (t) - f (t) = 2 t

\int e^{2 x + 1} d x

x \to 3 + lim (\frac{- x}{x - 3})

x \to 8 lim (\frac{3}{( x - 8 ) ^{2}})