What is the integral of-3x^4-6x^2+8 ?

The integral of-3x^4-6x^2+8 is -(3x^5)/5-2x^3+8x+C

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integral of-3x^4-6x^2+8

\int - 3 x^{4} - 6 x^{2} + 8 d x

- \frac{3 x ^{5}}{5} - 2 x^{3} + 8 x + C

Solution steps

\int - 3 x^{4} - 6 x^{2} + 8 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 3 x^{4} d x - \int 6 x^{2} d x + \int 8 d x

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

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

\int 8 d x = 8 x

= - \frac{3 x ^{5}}{5} - 2 x^{3} + 8 x

Add a constant to the solution

= - \frac{3 x ^{5}}{5} - 2 x^{3} + 8 x + C

x \to 0 lim (x csc (π x))

x \to \frac{1}{3} lim (x^{4})

x \to + 0 + lim (x^{x})

(x, y) \to (0, 0) lim (1)

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

What is the integral of-3x^4-6x^2+8 ?
The integral of-3x^4-6x^2+8 is -(3x^5)/5-2x^3+8x+C