What is the integral of-3x^2-6x+45 ?

The integral of-3x^2-6x+45 is -x^3-3x^2+45x+C

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integral of-3x^2-6x+45

\int - 3 x^{2} - 6 x + 45 d x

- x^{3} - 3 x^{2} + 45 x + C

Solution steps

\int - 3 x^{2} - 6 x + 45 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^{2} d x - \int 6 x d x + \int 45 d x

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

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

\int 45 d x = 45 x

= - x^{3} - 3 x^{2} + 45 x

Add a constant to the solution

= - x^{3} - 3 x^{2} + 45 x + C

f (x) = \frac{1}{x ^{4}}, at x = 1

\int \frac{6 x ^{5} + 2 x}{x ^{6} + x ^{2}} d x

\frac{d}{d x} (x^{\frac{4}{9}})

\int_{6}^{8} \frac{32}{( x - 6 ) ^{3}} d x

\frac{2 x}{x - 3}

What is the integral of-3x^2-6x+45 ?
The integral of-3x^2-6x+45 is -x^3-3x^2+45x+C