What is the integral of x(x-21)^2 ?

The integral of x(x-21)^2 is (x^4)/4-14x^3+(441x^2)/2+C

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integral of x(x-21)^2

\int x (x - 21)^{2} d x

\frac{x ^{4}}{4} - 14 x^{3} + \frac{441 x ^{2}}{2} + C

Solution steps

\int x (x - 21)^{2} d x

Expand

x (x - 21)^{2} : x^{3} - 42 x^{2} + 441 x

= \int x^{3} - 42 x^{2} + 441 x 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^{3} d x - \int 42 x^{2} d x + \int 441 x d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 42 x^{2} d x = 14 x^{3}

\int 441 x d x = \frac{441 x ^{2}}{2}

= \frac{x ^{4}}{4} - 14 x^{3} + \frac{441 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{4} - 14 x^{3} + \frac{441 x ^{2}}{2} + C

\int 3 sec (x) tan (x) d x

\int 4 sec (2 x) tan (2 x) d x

y = 2 x + 4

\frac{48}{x}

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

What is the integral of x(x-21)^2 ?
The integral of x(x-21)^2 is (x^4)/4-14x^3+(441x^2)/2+C