What is the integral of (t+200)^2 ?

The integral of (t+200)^2 is (t^3)/3+200t^2+40000t+C

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integral of (t+200)^2

\int (t + 200)^{2} d t

\frac{t ^{3}}{3} + 200 t^{2} + 40000 t + C

Solution steps

\int (t + 200)^{2} d t

Expand

(t + 200)^{2} : t^{2} + 400 t + 40000

= \int t^{2} + 400 t + 40000 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int t^{2} d t + \int 400 t d t + \int 40000 d t

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

\int 400 t d t = 200 t^{2}

\int 40000 d t = 40000 t

= \frac{t ^{3}}{3} + 200 t^{2} + 40000 t

Add a constant to the solution

= \frac{t ^{3}}{3} + 200 t^{2} + 40000 t + C

\frac{d}{d x} (\frac{2 - x e ^{x}}{x + e ^{x}})

y^{^{'''}} - 3 y^{^{''}} + 3 y^{^{'}} - y = x - 4 e^{x}

\int sin (2 x - 1) d x

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

\frac{\partial}{\partial y} (y)

What is the integral of (t+200)^2 ?
The integral of (t+200)^2 is (t^3)/3+200t^2+40000t+C