What is the integral of 4x^3+24x-1 ?

The integral of 4x^3+24x-1 is x^4+12x^2-x+C

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integral of 4x^3+24x-1

\int 4 x^{3} + 24 x - 1 d x

x^{4} + 12 x^{2} - x + C

Solution steps

\int 4 x^{3} + 24 x - 1 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^{3} d x + \int 24 x d x - \int 1 d x

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

\int 24 x d x = 12 x^{2}

\int 1 d x = x

= x^{4} + 12 x^{2} - x

Add a constant to the solution

= x^{4} + 12 x^{2} - x + C

x \to 3 lim (\frac{3 - ∣ x ∣}{x + 3})

y^{^{''}} + 2 k y^{^{'}} + a k^{2} y = 0

\frac{s + 3}{s ^{2} + 4 s + 8}

x \to - \infty lim (\frac{x}{x})

\frac{\partial}{\partial x} (- \frac{2 x}{( 1 + x ^{2} ) ^{2}})

What is the integral of 4x^3+24x-1 ?
The integral of 4x^3+24x-1 is x^4+12x^2-x+C