What is the integral of 3x^2-60x+400 ?

The integral of 3x^2-60x+400 is x^3-30x^2+400x+C

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integral of 3x^2-60x+400

\int 3 x^{2} - 60 x + 400 d x

x^{3} - 30 x^{2} + 400 x + C

Solution steps

\int 3 x^{2} - 60 x + 400 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 3 x^{2} d x - \int 60 x d x + \int 400 d x

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

\int 60 x d x = 30 x^{2}

\int 400 d x = 400 x

= x^{3} - 30 x^{2} + 400 x

Add a constant to the solution

= x^{3} - 30 x^{2} + 400 x + C

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What is the integral of 3x^2-60x+400 ?
The integral of 3x^2-60x+400 is x^3-30x^2+400x+C