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

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

\int x (1 + x) d x

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

Solution steps

\int x (1 + x) d x

Expand

x (1 + x) : x + x

= \int 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 x d x + \int x d x

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

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

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

Add a constant to the solution

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

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

\int sin (x - \frac{π}{2}) d x

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

\int 6 x^{5} - 4 x^{3} + 2 x - 10 d x

\int \frac{1}{5 x + 2} d x

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