What is the integral of (6-4xe^x)/x ?

The integral of (6-4xe^x)/x is 6ln|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 (6-4xe^x)/x

\int \frac{6 - 4 x e ^{x}}{x} d x

6 ln ∣ x ∣ - 4 e^{x} + C

Solution steps

\int \frac{6 - 4 x e ^{x}}{x} d x

Expand

\frac{6 - 4 x e ^{x}}{x} : \frac{6}{x} - 4 e^{x}

= \int \frac{6}{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{6}{x} d x - \int 4 e^{x} d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

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

= 6 ln ∣ x ∣ - 4 e^{x}

Add a constant to the solution

= 6 ln ∣ x ∣ - 4 e^{x} + C

8 x^{2}

\int \frac{- 2 x ^{3}}{x ^{3} + 1} d x

\int 8 x (4 x^{2} + 5)^{4} d x

\int 25 - 3 x d x

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

What is the integral of (6-4xe^x)/x ?
The integral of (6-4xe^x)/x is 6ln|x|-4e^x+C