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Popular >

integral of (x^3-6x)

Solution

\int (x^{3} - 6 x) d x

Solution

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

Solution steps

\int x^{3} - 6 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 6 x d x

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

\int 6 x d x = 3 x^{2}

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

Add a constant to the solution

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

Popular Examples

derivative of x^3-6x^2-15x+40

\frac{d}{d x} (x^{3} - 6 x^{2} - 15 x + 40)

limit as x approaches 0 of-7/(1-7x)

x \to 0 lim (- \frac{7}{1 - 7 x})

area y=x^2+2,(1,4)area

y = x^{2} + 2, (1, 4)

tangent of y=9cos(x),(pi/3 ,4.5)tangent of

y = 9 cos (x), (\frac{π}{3}, 4.5)

derivative of xe^{1/2 x}

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

Frequently Asked Questions (FAQ)

What is the integral of (x^3-6x) ?
The integral of (x^3-6x) is (x^4)/4-3x^2+C