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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

sum from n=1 to infinity of 3(1/2)^{n-1}

n = 1 \sum \infty 3 (\frac{1}{2})^{n - 1}

integral of (1+e^x)^2

\int (1 + e^{x})^{2} d x

derivative of-5t(2t^7-1)^5 derivative of

- 5 t (2 t^{7} - 1)^{5}

integral of e^{(pix)/4}

\int e^{\frac{π x}{4}} d x

limit as x approaches 3+of (ln(x))/(x-3)

x \to 3 + lim (\frac{ln ( x )}{x - 3})

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