What is the integral of 6(x-7)^2 ?

The integral of 6(x-7)^2 is 6((x^3)/3-7x^2+49x)+C

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integral of 6(x-7)^2

\int 6 (x - 7)^{2} d x

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

Solution steps

\int 6 (x - 7)^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int (x - 7)^{2} d x

Expand

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

= 6 \cdot \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

= 6 (\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

= 6 (\frac{x ^{3}}{3} - 7 x^{2} + 49 x)

Add a constant to the solution

= 6 (\frac{x ^{3}}{3} - 7 x^{2} + 49 x) + C

\int x e^{x} sin (x) d x

\frac{d}{d x} (\frac{3}{7} 5 x^{3})

x \to 0 + lim (7 x ln (x))

x \to 1 lim (e^{7 x^{5} - 7 x})

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

What is the integral of 6(x-7)^2 ?
The integral of 6(x-7)^2 is 6((x^3)/3-7x^2+49x)+C