What is the integral of 2sqrt(x)-x ?

The integral of 2sqrt(x)-x is 4/3 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

integral of 2sqrt(x)-x

\int 2 x - x d x

\frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + C

Solution steps

\int 2 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 2 x d x - \int x d x

\int 2 x d x = \frac{4}{3} x^{\frac{3}{2}}

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

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + C

t an g e n t y = x + 5, at x = 11

\int_{- 1}^{4} x - 2 x^{2} d x

f (x) = 2^{s i n (x)}

d er i v a t i v e y = (\frac{8}{x})^{5 x}

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

What is the integral of 2sqrt(x)-x ?
The integral of 2sqrt(x)-x is 4/3 x^{3/2}-(x^2)/2+C