What is the integral of 5^{-8(x-7)} ?

The integral of 5^{-8(x-7)} is -(390625^{-x+7})/(8ln(5))+C

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integral of 5^{-8(x-7)}

\int 5^{- 8 (x - 7)} d x

- \frac{39062 5 ^{- x + 7}}{8 ln ( 5 )} + C

Solution steps

\int 5^{- 8 (x - 7)} d x

Simplify

5^{- 8 (x - 7)} : 39062 5^{- x + 7}

= \int 39062 5^{- x + 7} d x

Apply u-substitution

: \int - 39062 5^{u} d u

= \int - 39062 5^{u} d u

Take the constant out:

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

= - \int 39062 5^{u} d u

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

= - \frac{39062 5 ^{u}}{ln ( 390625 )}

Substitute back

u = - x + 7

= - \frac{39062 5 ^{- x + 7}}{ln ( 390625 )}

Simplify

ln (390625) : 8 ln (5)

= - \frac{39062 5 ^{- x + 7}}{8 ln ( 5 )}

Add a constant to the solution

= - \frac{39062 5 ^{- x + 7}}{8 ln ( 5 )} + C

\int \frac{a}{a - x} d x

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

\frac{d}{d x} (x e^{x^{4}})

\frac{d}{d z} (x^{2} y z)

\int x^{5} \cdot ln (x) d x

What is the integral of 5^{-8(x-7)} ?
The integral of 5^{-8(x-7)} is -(390625^{-x+7})/(8ln(5))+C