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Popular >

integral of-1/2 x^3

Solution

\int - \frac{1}{2} x^{3} d x

Solution

- \frac{x ^{4}}{8} + C

Solution steps

\int - \frac{1}{2} x^{3} d x

Take the constant out:

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

= - \frac{1}{2} \cdot \int x^{3} d x

Apply the Power Rule

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

= - \frac{1}{2} \cdot \frac{x ^{4}}{4}

Simplify

- \frac{1}{2} \cdot \frac{x ^{4}}{4} : - \frac{x ^{4}}{8}

= - \frac{x ^{4}}{8}

Add a constant to the solution

= - \frac{x ^{4}}{8} + C

Popular Examples

integral of x^3*cos(x^4+2)

\int x^{3} \cdot cos (x^{4} + 2) d x

integral of x/(25)

\int \frac{x}{25} d x

integral of ((x^2+x+8))/((x^2+3x-4))

\int \frac{( x ^{2} + x + 8 )}{( x ^{2} + 3 x - 4 )} d x

integral of-2xsin(2x)

\int - 2 x sin (2 x) d x

integral of 2sin(x)e^{cos(x)}

\int 2 sin (x) e^{c o s (x)} d x

Frequently Asked Questions (FAQ)

What is the integral of-1/2 x^3 ?
The integral of-1/2 x^3 is -(x^4)/8+C