What is the integral of 2+4x+42x^2 ?

The integral of 2+4x+42x^2 is 2x+2x^2+14x^3+C

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integral of 2+4x+42x^2

\int 2 + 4 x + 42 x^{2} d x

2 x + 2 x^{2} + 14 x^{3} + C

Solution steps

\int 2 + 4 x + 42 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 2 d x + \int 4 x d x + \int 42 x^{2} d x

\int 2 d x = 2 x

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

\int 42 x^{2} d x = 14 x^{3}

= 2 x + 2 x^{2} + 14 x^{3}

Add a constant to the solution

= 2 x + 2 x^{2} + 14 x^{3} + C

\int \frac{2}{( x + 4 ) ( x + 6 )} d x

\int \frac{3}{4 x ^{2} - 1} d x

\int \frac{5}{x 4 x ^{4} - 9} d x

\int \frac{cos ( 3 x ) sin ( 3 x )}{3} d x

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

What is the integral of 2+4x+42x^2 ?
The integral of 2+4x+42x^2 is 2x+2x^2+14x^3+C