How do you integrate $\int 5^{- x} d x$ $int 5^-xdx$ ?

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Answer 1 · 2016-12-07T06:39:44

Using u-substitution:

Let $u = - x$ $u=-x$
$d u = - 1 d x$ $du=-1dx$

$= \int 5^{u} d u$ $=int5^udu$

$= \frac{5^{u}}{ln 5} \cdot - 1$ $=5^u/ln5*-1$

$= - \frac{5^{- x}}{ln 5}$ $=-5^(-x)/ln5$

$= - \frac{1}{5^{x} ln 5}$ $=-1/(5^xln5)$

How do you integrate ∫5−xdxint 5^-xdx?