What is the integral of (2/x-4e^x) ?

The integral of (2/x-4e^x) is 2ln|x|-4e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2/x-4e^x)

\int (\frac{2}{x} - 4 e^{x}) d x

2 ln ∣ x ∣ - 4 e^{x} + C

Solution steps

\int \frac{2}{x} - 4 e^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2}{x} d x - \int 4 e^{x} d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 4 e^{x} d x = 4 e^{x}

= 2 ln ∣ x ∣ - 4 e^{x}

Add a constant to the solution

= 2 ln ∣ x ∣ - 4 e^{x} + C

\frac{d}{d x} ((\frac{1}{x ^{2}}) d x)

4 x, x^{2}

\frac{d y}{d x} + y^{5} x + 5 y = 0

y = \frac{5 x ^{3}}{3} - x + 7 e^{x}

- 2 x^{3} + 23 x^{2} - 33 x - 108, [0, x]

What is the integral of (2/x-4e^x) ?
The integral of (2/x-4e^x) is 2ln|x|-4e^x+C