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Popular >

integral of x^3-9x

Solution

\int x^{3} - 9 x d x

Solution

\frac{x ^{4}}{4} - \frac{9 x ^{2}}{2} + C

Solution steps

\int x^{3} - 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^{3} d x - \int 9 x d x

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

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

= \frac{x ^{4}}{4} - \frac{9 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{9 x ^{2}}{2} + C

Popular Examples

derivative of sin(x+3+(-cos(x-1/2)))

\frac{d}{d x} (sin (x + 3) + (- cos (x - \frac{1}{2})))

integral from-2 to-1 of 6x^{-3}

\int_{- 2}^{- 1} 6 x^{- 3} d x

derivative of (x^2+x/(x+1))

\frac{d}{d x} (\frac{x ^{2} + x}{x + 1})

derivative of (x^2+2/(x^4-3x^2+1))

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{4} - 3 x ^{2} + 1})

y^{''}-4y^'+13y=0,y(0)=1,y^'(0)=4

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = 1, y^{^{'}} (0) = 4

Frequently Asked Questions (FAQ)

What is the integral of x^3-9x ?
The integral of x^3-9x is (x^4)/4-(9x^2)/2+C