What is the integral of c/x e^{-9x} ?

The integral of c/x e^{-9x} is c\Ei(-9x)+C

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integral of c/x e^{-9x}

\int \frac{c}{x} e^{- 9 x} d x

c Ei (- 9 x) + C

Solution steps

\int \frac{c}{x} e^{- 9 x} d x

Take the constant out:

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

= c \cdot \int \frac{1}{x} e^{- 9 x} d x

Simplify

\frac{1}{x} e^{- 9 x} : \frac{e ^{- 9 x}}{x}

= c \cdot \int \frac{e ^{- 9 x}}{x} d x

Apply u-substitution

= c \cdot \int \frac{e ^{u}}{u} d u

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= c Ei (u)

Substitute back

u = - 9 x

= c Ei (- 9 x)

Add a constant to the solution

= c Ei (- 9 x) + C

What is the integral of c/x e^{-9x} ?
The integral of c/x e^{-9x} is c\Ei(-9x)+C