What is the integral of 7e^{-t} ?

The integral of 7e^{-t} is -7e^{-t}+C

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integral of 7e^{-t}

\int 7 e^{- t} d t

- 7 e^{- t} + C

Solution steps

\int 7 e^{- t} d t

Take the constant out:

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

= 7 \cdot \int e^{- t} d t

Apply u-substitution

: \int - e^{u} d u

= 7 \cdot \int - e^{u} d u

Take the constant out:

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

= 7 (- \int e^{u} d u)

Use the common integral:

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

= 7 (- e^{u})

Substitute back

u = - t

= 7 (- e^{- t})

Simplify

= - 7 e^{- t}

Add a constant to the solution

= - 7 e^{- t} + C

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

(x + 1) y^{^{'}} = x^{2} - y

\int \frac{9}{x ^{2} + 1} d x

(\frac{x}{1 - x})^{^{'}}

y^{^{''}} - 8 y^{^{'}} + 20 y = 200 x^{2} - 52 x e^{x}