What is the integral of-4x^2-4x+48 ?

The integral of-4x^2-4x+48 is -(4x^3)/3-2x^2+48x+C

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integral of-4x^2-4x+48

\int - 4 x^{2} - 4 x + 48 d x

- \frac{4 x ^{3}}{3} - 2 x^{2} + 48 x + C

Solution steps

\int - 4 x^{2} - 4 x + 48 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^{2} d x - \int 4 x d x + \int 48 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 4 x d x = 2 x^{2}

\int 48 d x = 48 x

= - \frac{4 x ^{3}}{3} - 2 x^{2} + 48 x

Add a constant to the solution

= - \frac{4 x ^{3}}{3} - 2 x^{2} + 48 x + C

x \to 0 + lim (ln (\frac{7}{x ^{3}}))

\int \frac{1}{x} - x d x

y = \frac{3}{x}, (- 2, - \frac{3}{2})

\int x^{\frac{1}{9}} d x

\int (x + 1) sec (x^{2} + 2 x) tan (x^{2} + 2 x) d x

What is the integral of-4x^2-4x+48 ?
The integral of-4x^2-4x+48 is -(4x^3)/3-2x^2+48x+C