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

\frac{d}{d x} (2.1 + e^{2} - \frac{π ^{2}}{20})

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

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

\frac{d}{d x} (\frac{3}{x + 3})

x \to 0 + lim (x^{16 x})