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Popular >

integral of (x-10)^2

Solution

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

Solution

\frac{x ^{3}}{3} - 10 x^{2} + 100 x + C

Solution steps

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

Expand

(x - 10)^{2} : x^{2} - 20 x + 100

= \int x^{2} - 20 x + 100 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^{2} d x - \int 20 x d x + \int 100 d x

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

\int 20 x d x = 10 x^{2}

\int 100 d x = 100 x

= \frac{x ^{3}}{3} - 10 x^{2} + 100 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 10 x^{2} + 100 x + C

Popular Examples

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x \to - 8 lim (\frac{2 x}{x + 8})

y^{''}-6y^'+9y=18x^2+6-12e^{3x}

y^{^{''}} - 6 y^{^{'}} + 9 y = 18 x^{2} + 6 - 12 e^{3 x}

derivative of y=3x+7 derivative of

y = 3 x + 7

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\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{4} - 1})

derivative of-0.05(t+1.1)^{2.2}+0.7t+0.9 derivative of

- 0.05 (t + 1.1)^{2.2} + 0.7 t + 0.9

Frequently Asked Questions (FAQ)

What is the integral of (x-10)^2 ?
The integral of (x-10)^2 is (x^3)/3-10x^2+100x+C