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

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

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integral of (-3x^2+2x+5)

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

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

\frac{d}{d x} (2 x^{3} + 6 x y^{2} - 3 x^{2} + 3 y^{2})

cos (3 x), 2.5

1 - t

\int \frac{x + 3}{x + 3} d x

\int sin (x) cos (x) e^{x} d x

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