What is the integral of 7^{-2x} ?

The integral of 7^{-2x} is -(49^{-x})/(2ln(7))+C

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integral of 7^{-2x}

\int 7^{- 2 x} d x

- \frac{4 9 ^{- x}}{2 ln ( 7 )} + C

Solution steps

\int 7^{- 2 x} d x

Apply u-substitution

: \int - \frac{1}{2} \cdot 7^{u} d u

= \int - \frac{1}{2} \cdot 7^{u} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int 7^{u} d u

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

= - \frac{1}{2} \cdot \frac{7 ^{u}}{ln ( 7 )}

Substitute back

u = - 2 x

= - \frac{1}{2} \cdot \frac{7 ^{- 2 x}}{ln ( 7 )}

Simplify

- \frac{1}{2} \cdot \frac{7 ^{- 2 x}}{ln ( 7 )} : - \frac{4 9 ^{- x}}{2 ln ( 7 )}

= - \frac{4 9 ^{- x}}{2 ln ( 7 )}

Add a constant to the solution

= - \frac{4 9 ^{- x}}{2 ln ( 7 )} + C

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What is the integral of 7^{-2x} ?
The integral of 7^{-2x} is -(49^{-x})/(2ln(7))+C