What is the integral of x^5-3x+2/x ?

The integral of x^5-3x+2/x is (x^6)/6-(3x^2)/2+2ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^5-3x+2/x

\int x^{5} - 3 x + \frac{2}{x} d x

\frac{x ^{6}}{6} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣ + C

Solution steps

\int x^{5} - 3 x + \frac{2}{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 x^{5} d x - \int 3 x d x + \int \frac{2}{x} d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 3 x d x = \frac{3 x ^{2}}{2}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{6}}{6} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{6}}{6} - \frac{3 x ^{2}}{2} + 2 ln ∣ x ∣ + C

What is the integral of x^5-3x+2/x ?
The integral of x^5-3x+2/x is (x^6)/6-(3x^2)/2+2ln|x|+C