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

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

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

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

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

Solution steps

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

\int 1 d x = x

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

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

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

Add a constant to the solution

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

\int \frac{3}{x + x} d x

\int 7 x x^{2} - 1 d x

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

\int \frac{1}{( 2 x - 1 ) ( 2 x + 1 )} d x

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

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