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

The integral of x(sqrt(x)-3) is 2/5 x^{5/2}-(3x^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 x(sqrt(x)-3)

\int x (x - 3) d x

\frac{2}{5} x^{\frac{5}{2}} - \frac{3 x ^{2}}{2} + C

Solution steps

\int x (x - 3) d x

Expand

x (x - 3) : x^{\frac{3}{2}} - 3 x

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

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

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

= \frac{2}{5} x^{\frac{5}{2}} - \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - \frac{3 x ^{2}}{2} + C

\frac{d}{d x} (3 - 3 x^{2})

f (x) = - \frac{7}{( x + 4 ) ^{2}}

f (t) = (1) (t^{3})

\frac{d}{d x} (\frac{1}{16 x ^{4}})

- 3 y^{^{'}} + \frac{3 y}{x} = x y^{4}

What is the integral of x(sqrt(x)-3) ?
The integral of x(sqrt(x)-3) is 2/5 x^{5/2}-(3x^2)/2+C