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Popular >

integral of (x^3-3x)

Solution

\int (x^{3} - 3 x) d x

Solution

\frac{x ^{4}}{4} - \frac{3 x ^{2}}{2} + C

Solution steps

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

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

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

= \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{3 x ^{2}}{2} + C

Popular Examples

integral from 2 to 5 of e^{5x}

\int_{2}^{5} e^{5 x} d x

limit as x approaches 1 of 3ln(x)+4

x \to 1 lim (3 ln (x) + 4)

integral of-t+2

\int - t + 2 d t

(dy}{dx}=\frac{-4sin(x)cos(x))/y

\frac{d y}{d x} = \frac{- 4 sin ( x ) cos ( x )}{y}

integral of v(v^2+2)^2

\int v (v^{2} + 2)^{2} d v

Frequently Asked Questions (FAQ)

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