What is the integral of x^2+3x+2 ?

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

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integral of x^2+3x+2

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

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

t - e^{- 3 t}

\frac{\partial}{\partial x} (\frac{- 3}{y - 3 x})

2 x^{2} + x - 1, at a = 0

\int_{0}^{3} x^{3} - x d x

f (x) = (4 x^{4} - 7 x^{2} + 6)

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