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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

: \int \frac{e ^{u}}{u} d u

= 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

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

f (x) = x^{5 x}

y = x^{4} + 9 e^{x}, (0, 9)

2 y d x + (y - 2 x) d y = 0

y = (3 x^{2}) (5 x^{4})

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