What is the integral of 10+6x+24x^2 ?

The integral of 10+6x+24x^2 is 10x+3x^2+8x^3+C

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integral of 10+6x+24x^2

\int 10 + 6 x + 24 x^{2} d x

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

Solution steps

\int 10 + 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 10 d x + \int 6 x d x + \int 24 x^{2} d x

\int 10 d x = 10 x

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

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

= 10 x + 3 x^{2} + 8 x^{3}

Add a constant to the solution

= 10 x + 3 x^{2} + 8 x^{3} + C

\frac{d}{d x} (- 2 cos^{2} (x))

x \to 0 lim (\frac{2}{tan ( x )})

\int_{6}^{8} \frac{78}{( x - 6 ) ^{3}} d x

\int \frac{2 x ^{3} + 6 x + 3}{( x + 2 ) ^{2} ( x ^{2} + 1 )} d x

\int (t^{2} + t) e^{t^{3}} + 3^{t} d t

What is the integral of 10+6x+24x^2 ?
The integral of 10+6x+24x^2 is 10x+3x^2+8x^3+C