What is the integral of 4+6x+24x^2 ?

The integral of 4+6x+24x^2 is 4x+3x^2+8x^3+C

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integral of 4+6x+24x^2

\int 4 + 6 x + 24 x^{2} d x

4 x + 3 x^{2} + 8 x^{3} + C

Solution steps

\int 4 + 6 x + 24 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 4 d x + \int 6 x d x + \int 24 x^{2} d x

\int 4 d x = 4 x

\int 6 x d x = 3 x^{2}

\int 24 x^{2} d x = 8 x^{3}

= 4 x + 3 x^{2} + 8 x^{3}

Add a constant to the solution

= 4 x + 3 x^{2} + 8 x^{3} + C

n = 1 \sum \infty \frac{n ^{7}}{6 ^{n}}

\int \frac{( x ^{2} - 49 )}{x ^{3}} d x

ln (1 - 2 y)

\frac{\partial}{\partial x} (2 x + 2 x y)

(x + 2 y) d x + (2 x + y) d y = 0

What is the integral of 4+6x+24x^2 ?
The integral of 4+6x+24x^2 is 4x+3x^2+8x^3+C