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

The integral of sqrt(x)+x^2 is 2/3 x^{3/2}+(x^3)/3+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)+x^2

\int x + x^{2} d x

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

Solution steps

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

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

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

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

Add a constant to the solution

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

y = 5 x^{4} + 3 x - 6, (1, 2)

\frac{\partial}{\partial y} (\frac{5 x y}{10 x - y})

\int_{- 8}^{8} (64 - x^{2}) d x

\frac{2}{( s + 3 )}

\frac{d}{d x} (\frac{1}{sin ( 3 x )})

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