What is the integral of ((x-1)^2)/(sqrt(x)) ?

The integral of ((x-1)^2)/(sqrt(x)) is 2/5 x^{5/2}-4/3 x^{3/2}+2sqrt(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((x-1)^2)/(sqrt(x))

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

\frac{2}{5} x^{\frac{5}{2}} - \frac{4}{3} x^{\frac{3}{2}} + 2 x + C

Solution steps

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

Expand

\frac{( x - 1 ) ^{2}}{x} : x^{\frac{3}{2}} - 2 x + \frac{1}{x}

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

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

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

\int \frac{1}{x} d x = 2 x

= \frac{2}{5} x^{\frac{5}{2}} - \frac{4}{3} x^{\frac{3}{2}} + 2 x

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - \frac{4}{3} x^{\frac{3}{2}} + 2 x + C

\int 3 tan^{3} (x) sec (x) d x

\int x^{- 4} x d x

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

\int \frac{1}{e ^{2 x} + 6} d x

\int sin (x) - sin^{3} (x) d x

What is the integral of ((x-1)^2)/(sqrt(x)) ?
The integral of ((x-1)^2)/(sqrt(x)) is 2/5 x^{5/2}-4/3 x^{3/2}+2sqrt(x)+C