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Popular >

integral of-2x^3

Solution

\int - 2 x^{3} d x

Solution

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

Solution steps

\int - 2 x^{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

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

Simplify

- 2 \cdot \frac{x ^{4}}{4} : - \frac{x ^{4}}{2}

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

Add a constant to the solution

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

Popular Examples

derivative of 2arctan(sqrt(x))

\frac{d}{d x} (2 arctan (x))

(\partial}{\partial x}(\frac{x^2)/2+(y^3)/3)

\frac{\partial}{\partial x} (\frac{x ^{2}}{2} + \frac{y ^{3}}{3})

derivative of f(x)=5ex derivative of

f (x) = 5 e x

d/(dt)(t^{1/2})

\frac{d}{d t} (t^{\frac{1}{2}})

limit as x approaches 0 of ((3+x^2)-9)/x

x \to 0 lim (\frac{( 3 + x ^{2} ) - 9}{x})

Frequently Asked Questions (FAQ)

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