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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/x+sqrt(x)

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

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

Solution steps

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

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

Add a constant to the solution

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

\frac{d y}{d x} = 2 x y + 3 x^{2} e^{x^{2}}

\frac{d}{d a} (cos (a) tan (a))

x \to 1 lim (2 x - 3)

\int \frac{4}{x ^{2} x ^{2} + 4} d x

2 y \frac{d y}{d x} + 8 x = 6

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