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Popular >

integral of (x-5)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

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

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

\int 25 d x = 25 x

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

Add a constant to the solution

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

Popular Examples

integral from 1 to 3 of x^3ln(x)

\int_{1}^{3} x^{3} ln (x) d x

derivative of (3x/(2x+1))

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

integral of (6x+5)/(6x^2)

\int \frac{6 x + 5}{6 x ^{2}} d x

sum from n=1 to infinity of-1/n

n = 1 \sum \infty - \frac{1}{n}

derivative of x*ln^2(x)

\frac{d}{d x} (x \cdot ln^{2} (x))

Frequently Asked Questions (FAQ)

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