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

The integral of 3x^2-4x+2 is x^3-2x^2+2x+C

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integral of 3x^2-4x+2

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

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

Solution steps

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

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

\int 4 x d x = 2 x^{2}

\int 2 d x = 2 x

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

Add a constant to the solution

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

y^{^{'}} = \frac{y ^{4} + 3}{4 x y ^{3}}

\int \frac{1}{4 e ^{- 7 x} + e ^{7 x}} d x

\frac{\partial}{\partial x} (ln (x) + ln (y))

\int x^{3} (8^{- x^{4}}) d x

\frac{d}{d x} ((2 x^{4} - 7 x^{3} + 2 x - 1)^{2})