What is the integral of (3x^2+2x+4) ?

The integral of (3x^2+2x+4) is x^3+x^2+4x+C

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integral of (3x^2+2x+4)

\int (3 x^{2} + 2 x + 4) d x

x^{3} + x^{2} + 4 x + C

Solution steps

\int 3 x^{2} + 2 x + 4 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 2 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

= x^{3} + x^{2} + 4 x

Add a constant to the solution

= x^{3} + x^{2} + 4 x + C

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\int 5 x^{2} cos (3 x) d x

\int 7 x^{8} - 0^{2} (2 x^{3}) d x

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