What is the integral of 7^{-3x} ?

The integral of 7^{-3x} is -(343^{-x})/(3ln(7))+C

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integral of 7^{-3x}

\int 7^{- 3 x} d x

- \frac{34 3 ^{- x}}{3 ln ( 7 )} + C

Solution steps

\int 7^{- 3 x} d x

Simplify

7^{- 3 x} : 34 3^{- x}

= \int 34 3^{- x} d x

Apply u-substitution

: \int - 34 3^{u} d u

= \int - 34 3^{u} d u

Take the constant out:

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

= - \int 34 3^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - \frac{34 3 ^{u}}{ln ( 343 )}

Substitute back

u = - x

= - \frac{34 3 ^{- x}}{ln ( 343 )}

Simplify

ln (343) : 3 ln (7)

= - \frac{34 3 ^{- x}}{3 ln ( 7 )}

Add a constant to the solution

= - \frac{34 3 ^{- x}}{3 ln ( 7 )} + C

\int \frac{1}{1 + 5 x} d x

(\frac{d y}{d x}) = e^{(4 x + 5 y)}

\frac{x}{2} + \frac{2}{x}

y^{^{'}} = \frac{y}{x ^{2}}

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

What is the integral of 7^{-3x} ?
The integral of 7^{-3x} is -(343^{-x})/(3ln(7))+C