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Popular >

integral of (x-7)^2

Solution

\int (x - 7)^{2} d x

Solution

\frac{x ^{3}}{3} - 7 x^{2} + 49 x + C

Solution steps

\int (x - 7)^{2} d x

Expand

(x - 7)^{2} : x^{2} - 14 x + 49

= \int x^{2} - 14 x + 49 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 14 x d x + \int 49 d x

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

\int 14 x d x = 7 x^{2}

\int 49 d x = 49 x

= \frac{x ^{3}}{3} - 7 x^{2} + 49 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 7 x^{2} + 49 x + C

Popular Examples

sum from n=1 to infinity of 1/(2^{n-1)}

n = 1 \sum \infty \frac{1}{2 ^{n - 1}}

limit as x approaches infinity of 0^0

x \to \infty lim (0^{0})

limit as x approaches 3 of 1/((x-3))

x \to 3 lim (\frac{1}{( x - 3 )})

integral from 0 to 1 of 2x^2(x^3-1)^3

\int_{0}^{1} 2 x^{2} (x^{3} - 1)^{3} d x

integral of x^2-16

\int x^{2} - 16 d x

Frequently Asked Questions (FAQ)

What is the integral of (x-7)^2 ?
The integral of (x-7)^2 is (x^3)/3-7x^2+49x+C