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Popular >

integral of-x^2+4x-3

Solution

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

Solution

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Popular Examples

derivative of 9tan(x)

\frac{d}{d x} (9 tan (x))

(\partial)/(\partial x)((10x)/(1+x^2-y))

\frac{\partial}{\partial x} (\frac{10 x}{1 + x ^{2} - y})

(\partial)/(\partial y)(y/2)

\frac{\partial}{\partial y} (\frac{y}{2})

derivative of f(x)=3x^2-1 derivative of

f (x) = 3 x^{2} - 1

(dy)/(dx)=x+6y,y(0)=2

\frac{d y}{d x} = x + 6 y, y (0) = 2

Frequently Asked Questions (FAQ)

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