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

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

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integral of 4x+3x^2+12x^3+C

\int 4 x + 3 x^{2} + 12 x^{3} + C d x

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

Solution steps

\int 4 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 4 x d x + \int 3 x^{2} d x + \int 12 x^{3} d x + \int C d x

\int 4 x d x = 2 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

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

Add a constant to the solution

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

\int \frac{cos ( π \cdot x )}{sin ( π \cdot x )} d x

\frac{d y}{d x} = e^{2 x + y}

\frac{d y}{d x} = x e^{x^{2} - l n (y^{2})}

\int_{- 2}^{3} (10 x^{3} - 4 x) (x + 2) d x

f (x) = x sin (\frac{2}{x})

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