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Popular Calculus >

integral of x^3-4x

Solution

\int x^{3} - 4 x d x

Solution

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

Solution steps

\int x^{3} - 4 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 4 x d x

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

Graph

Popular Examples

integral of sin^9(x)cos^5(x)

\int sin^{9} (x) cos^{5} (x) d x

derivative of \sqrt[3]{x^2-1}

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

(dy)/(dx)= x/(y^2)

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

integral of (x^2+3)^2

\int (x^{2} + 3)^{2} d x

derivative of 6x^{2/3}

d er i v a t i v e 6 x^{\frac{2}{3}}

Frequently Asked Questions (FAQ)

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