What is the integral of ge^{-2ct} ?

The integral of ge^{-2ct} is -ge^{-2ct} 1/(2c)+C

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integral of ge^{-2ct}

\int g e^{- 2 c t} d t

- g e^{- 2 c t} \frac{1}{2 c} + C

Solution steps

\int g e^{- 2 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^{- 2 c t} d t

Apply u-substitution

: \int - \frac{e ^{u}}{2 c} d u

= g \cdot \int - \frac{e ^{u}}{2 c} d u

Take the constant out:

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

= g (- \frac{1}{2 c} \cdot \int e^{u} d u)

Use the common integral:

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

= g (- \frac{1}{2 c} e^{u})

Substitute back

u = - 2 c t

= g (- \frac{1}{2 c} e^{- 2 c t})

Simplify

= - g e^{- 2 c t} \frac{1}{2 c}

Add a constant to the solution

= - g e^{- 2 c t} \frac{1}{2 c} + C

x \to - 1 lim (\frac{x + 1}{1 - x ^{2}})

x \to 5 + lim (\frac{5}{x - 5})

\int cos (2 x) sin (3 x) d x

x^{\frac{1}{3}}, 8

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

What is the integral of ge^{-2ct} ?
The integral of ge^{-2ct} is -ge^{-2ct} 1/(2c)+C