What is the integral of (4e^x-5/x) ?

The integral of (4e^x-5/x) is 4e^x-5ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4e^x-5/x)

\int (4 e^{x} - \frac{5}{x}) d x

4 e^{x} - 5 ln ∣ x ∣ + C

Solution steps

\int 4 e^{x} - \frac{5}{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 4 e^{x} d x - \int \frac{5}{x} d x

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= 4 e^{x} - 5 ln ∣ x ∣

Add a constant to the solution

= 4 e^{x} - 5 ln ∣ x ∣ + C

x \to - 1 lim (\frac{\frac{1}{x} + 1}{x + 1})

\int_{- 2}^{2} (4 - x^{2})^{2} d x

\int_{- 1}^{1} \frac{1}{x + 2} d x

\int_{1}^{2} \frac{x + 1}{x} d x

\frac{d ^{4} y}{d x ^{4}} - 23 \frac{d ^{2} y}{d x ^{2}} - 50 y = 0

What is the integral of (4e^x-5/x) ?
The integral of (4e^x-5/x) is 4e^x-5ln|x|+C