What is the integral of 6x+3x^2+12x^3+C ?

The integral of 6x+3x^2+12x^3+C is 3x^2+x^3+3x^4+Cx+C

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integral of 6x+3x^2+12x^3+C

\int 6 x + 3 x^{2} + 12 x^{3} + C d x

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

Solution steps

\int 6 x + 3 x^{2} + 12 x^{3} + C 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 6 x d x + \int 3 x^{2} d x + \int 12 x^{3} d x + \int C d x

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

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

\int 12 x^{3} d x = 3 x^{4}

\int C d x = C x

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

Add a constant to the solution

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

\frac{( 3 t ^{2} + 4 )}{4 t + 4}

\int \frac{csc ( θ ) cot ( θ )}{9} d θ

\frac{d}{d x} (ln (1 + 7 x))

\frac{d}{d x} (x^{2} 4 x - 9)

\int - cos (u) + \frac{1}{3} cos^{3} (u) d u

What is the integral of 6x+3x^2+12x^3+C ?
The integral of 6x+3x^2+12x^3+C is 3x^2+x^3+3x^4+Cx+C