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Popular >

integral of-x^2+9x

Solution

\int - x^{2} + 9 x d x

Solution

- \frac{x ^{3}}{3} + \frac{9 x ^{2}}{2} + C

Solution steps

\int - x^{2} + 9 x 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 9 x d x

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

\int 9 x d x = \frac{9 x ^{2}}{2}

= - \frac{x ^{3}}{3} + \frac{9 x ^{2}}{2}

Add a constant to the solution

= - \frac{x ^{3}}{3} + \frac{9 x ^{2}}{2} + C

Popular Examples

y^{''}-2y^'-36y=0

y^{^{''}} - 2 y^{^{'}} - 36 y = 0

integral of x/(2x^2+x+3)

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

y^{^{'}} = 3 y, y (0) = 2

integral from 2 to infinity of e^{-x}

\int_{2}^{\infty} e^{- x} d x

(\partial)/(\partial x)((sin(x-y))(-1.1))

\frac{\partial}{\partial x} ((sin (x - y)) (- 1.1))

Frequently Asked Questions (FAQ)

What is the integral of-x^2+9x ?
The integral of-x^2+9x is -(x^3)/3+(9x^2)/2+C