What is the integral of (2+sqrt(x))/(sqrt(x)) ?

The integral of (2+sqrt(x))/(sqrt(x)) is 4sqrt(x)+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2+sqrt(x))/(sqrt(x))

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

4 x + x + C

Solution steps

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

Expand

\frac{2 + x}{x} : \frac{2}{x} + 1

= \int \frac{2}{x} + 1 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{2}{x} d x + \int 1 d x

\int \frac{2}{x} d x = 4 x

\int 1 d x = x

= 4 x + x

Add a constant to the solution

= 4 x + x + C

- 0.4 x^{2}

\int (\frac{7 x ^{6} - 8 x ^{4} + 9 x ^{3}}{2 x ^{2}}) d x

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

\int \frac{x ^{2}}{9 + x} d x

\int \frac{x + 1}{3 x ^{2} + 6 x - 5} d x

What is the integral of (2+sqrt(x))/(sqrt(x)) ?
The integral of (2+sqrt(x))/(sqrt(x)) is 4sqrt(x)+x+C