What is the integral of (5x^4+12x^3+6x-2) ?

The integral of (5x^4+12x^3+6x-2) is x^5+3x^4+3x^2-2x+C

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integral of (5x^4+12x^3+6x-2)

\int (5 x^{4} + 12 x^{3} + 6 x - 2) d x

x^{5} + 3 x^{4} + 3 x^{2} - 2 x + C

Solution steps

\int 5 x^{4} + 12 x^{3} + 6 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 5 x^{4} d x + \int 12 x^{3} d x + \int 6 x d x - \int 2 d x

\int 5 x^{4} d x = x^{5}

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

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

\int 2 d x = 2 x

= x^{5} + 3 x^{4} + 3 x^{2} - 2 x

Add a constant to the solution

= x^{5} + 3 x^{4} + 3 x^{2} - 2 x + C

(2 y + 2 t - 3) d t + (8 y + 2 t - 1) d y = 0

\frac{1}{3} (16 + x^{2})^{\frac{3}{2}} + \frac{16}{3}

\frac{d}{d x} (\frac{x ^{2} + 4 x + 13}{x + 2})

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

x \to - 3 lim (- x^{2} + 6 x - 5)

What is the integral of (5x^4+12x^3+6x-2) ?
The integral of (5x^4+12x^3+6x-2) is x^5+3x^4+3x^2-2x+C