What is the integral of x(x+5)^2 ?

The integral of x(x+5)^2 is (x^4)/4+(10x^3)/3+(25x^2)/2+C

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integral of x(x+5)^2

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

\frac{x ^{4}}{4} + \frac{10 x ^{3}}{3} + \frac{25 x ^{2}}{2} + C

Solution steps

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

Expand

x (x + 5)^{2} : x^{3} + 10 x^{2} + 25 x

= \int x^{3} + 10 x^{2} + 25 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 10 x^{2} d x + \int 25 x d x

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

\int 10 x^{2} d x = \frac{10 x ^{3}}{3}

\int 25 x d x = \frac{25 x ^{2}}{2}

= \frac{x ^{4}}{4} + \frac{10 x ^{3}}{3} + \frac{25 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{10 x ^{3}}{3} + \frac{25 x ^{2}}{2} + C

x y^{^{'}} = 1 - y^{2}

f (x) = - 2 ln (x)

x \to \infty lim (9 + \frac{4}{x})

\frac{d}{d x} (- 512 sin (2 x))

\int (1 - \frac{x ^{2}}{4} - \frac{y ^{2}}{9}) d x

What is the integral of x(x+5)^2 ?
The integral of x(x+5)^2 is (x^4)/4+(10x^3)/3+(25x^2)/2+C