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

The integral of (5-x)^2 is 25x-5x^2+(x^3)/3+C

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integral of (5-x)^2

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

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

Solution steps

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

Expand

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

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

\int 25 d x = 25 x

\int 10 x d x = 5 x^{2}

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

= 25 x - 5 x^{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= 25 x - 5 x^{2} + \frac{x ^{3}}{3} + C

f (x) = x^{2} - 2 x - 4, at x = 2

\frac{\partial}{\partial t} (sin (x - a t))

cos (2 t) (1 + e^{- 3 t})

\frac{d}{d x} ((x^{3} + 1)^{5})

\frac{\partial}{\partial x} (e^{- \frac{1}{x}})