What is the integral of (-3)/(7e^{7x)} ?

The integral of (-3)/(7e^{7x)} is 3/49 e^{-7x}+C

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integral of (-3)/(7e^{7x)}

\int \frac{- 3}{7 e ^{7 x}} d x

\frac{3}{49} e^{- 7 x} + C

Solution steps

\int \frac{- 3}{7 e ^{7 x}} d x

Take the constant out:

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

= \frac{- 3}{7} \cdot \int \frac{1}{e ^{7 x}} d x

Simplify

= (- \frac{3}{7}) \cdot \int \frac{1}{e ^{7 x}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{e ^{7 x}} = e^{- 7 x}

= (- \frac{3}{7}) \cdot \int e^{- 7 x} d x

Apply u-substitution

: \int - \frac{1}{7} e^{u} d u

= (- \frac{3}{7}) \cdot \int - \frac{1}{7} e^{u} d u

Take the constant out:

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

= (- \frac{3}{7}) (- \frac{1}{7} \cdot \int e^{u} d u)

Use the common integral:

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

= (- \frac{3}{7}) (- \frac{1}{7} e^{u})

Substitute back

u = - 7 x

= (- \frac{3}{7}) (- \frac{1}{7} e^{- 7 x})

Simplify

(- \frac{3}{7}) (- \frac{1}{7} e^{- 7 x}) : \frac{3}{49} e^{- 7 x}

= \frac{3}{49} e^{- 7 x}

Add a constant to the solution

= \frac{3}{49} e^{- 7 x} + C

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

y = 4 x, y = 3 x^{2}

x \frac{d y}{d x} - 3 y = 6

\int_{- \frac{π}{6}}^{0} 8 sec^{3} (x) d x

\frac{\partial}{\partial x} (ln (\frac{k}{x}))

What is the integral of (-3)/(7e^{7x)} ?
The integral of (-3)/(7e^{7x)} is 3/49 e^{-7x}+C