What is the integral of sqrt(x)+1/x ?

The integral of sqrt(x)+1/x is 2/3 x^{3/2}+ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(x)+1/x

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

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

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

Add a constant to the solution

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

\int (5 x - \frac{x ^{3}}{2} + \frac{A R y x ^{2}}{2} + C) d x

\int \frac{8}{x ^{3} + 4 x} d x

\int tan^{5} (\frac{x}{3}) d x

\int \frac{y ^{2} + 10 y + 25}{( y ^{2} + 25 ) ^{2}} d y

\int (3 x^{8} - x^{9}) ln (x) d x

What is the integral of sqrt(x)+1/x ?
The integral of sqrt(x)+1/x is 2/3 x^{3/2}+ln|x|+C