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Popular >

integral of x^3-x

Solution

\int x^{3} - x d x

Solution

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

Solution steps

\int x^{3} - 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 x d x

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

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

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial x)(sqrt(5x^2+y^2))

\frac{\partial}{\partial x} (5 x^{2} + y^{2})

integral of 3cos(x/2)

\int 3 cos (\frac{x}{2}) d x

integral of 1/((8-x)^2)

\int \frac{1}{( 8 - x ) ^{2}} d x

derivative of (3-2sin(x)^5)

\frac{d}{d x} ((3 - 2 sin (x))^{5})

limit as x approaches-infinity of x,2

x \to - \infty lim (x, 2)

Frequently Asked Questions (FAQ)

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