What is the integral of ((sqrt(x)-5)^2-x)^2 ?

The integral of ((sqrt(x)-5)^2-x)^2 is 50x^2-1000/3 x^{3/2}+625x+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)-5)^2-x)^2

\int ((x - 5)^{2} - x)^{2} d x

50 x^{2} - \frac{1000}{3} x^{\frac{3}{2}} + 625 x + C

Solution steps

\int ((x - 5)^{2} - x)^{2} d x

Expand

(x - 5)^{2} - x : - 10 x + 25

= \int (- 10 x + 25)^{2} d x

Expand

(- 10 x + 25)^{2} : 100 x - 500 x + 625

= \int 100 x - 500 x + 625 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 100 x d x - \int 500 x d x + \int 625 d x

\int 100 x d x = 50 x^{2}

\int 500 x d x = \frac{1000}{3} x^{\frac{3}{2}}

\int 625 d x = 625 x

= 50 x^{2} - \frac{1000}{3} x^{\frac{3}{2}} + 625 x

Add a constant to the solution

= 50 x^{2} - \frac{1000}{3} x^{\frac{3}{2}} + 625 x + C

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

\int (x^{3} - sec^{2} (x)) d x

\int \frac{( x ^{3} )}{x ^{2} + 1} d x

\int t sec^{2} (t) d t

\int 3 x^{2} cos (0.5 x) d x

What is the integral of ((sqrt(x)-5)^2-x)^2 ?
The integral of ((sqrt(x)-5)^2-x)^2 is 50x^2-1000/3 x^{3/2}+625x+C