What is the integral of 3+sqrt(x) ?

The integral of 3+sqrt(x) is 3x+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 3+sqrt(x)

\int 3 + x d x

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

Solution steps

\int 3 + 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 3 d x + \int x d x

\int 3 d x = 3 x

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

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

Add a constant to the solution

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

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

\int \frac{4 x ^{2}}{1 + x ^{3}} d x

\int 3 y 3 2 y^{2} - 8 d y

\frac{d}{d x} (e^{2 (x - 1)^{2}})

f (x) = 0.3 x^{1.2}

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