What is the integral of (3x^2+2x+1) ?

The integral of (3x^2+2x+1) is x^3+x^2+x+C

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integral of (3x^2+2x+1)

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

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

Solution steps

\int 3 x^{2} + 2 x + 1 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 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\frac{\partial}{\partial z} (2 x z)

\int \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

\frac{\partial}{\partial x} (3 x^{2} + 2 y^{2})

y = x^{2} - 3 x, y = 4 x

(x^{2} + 1) \frac{d y}{d x} + 7 x (y - 1) = 0, y (0) = 9

What is the integral of (3x^2+2x+1) ?
The integral of (3x^2+2x+1) is x^3+x^2+x+C