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Popular >

integral of (-x)/2

Solution

\int \frac{- x}{2} d x

Solution

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

Solution steps

\int \frac{- x}{2} 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 d x

Simplify

= (- \frac{1}{2}) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= (- \frac{1}{2}) \frac{x ^{2}}{2}

Simplify

(- \frac{1}{2}) \frac{x ^{2}}{2} : - \frac{x ^{2}}{4}

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

Add a constant to the solution

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

Popular Examples

integral of (11)/(ax+

\int \frac{11}{a x + d} d x

integral of (6+3x)/(1+x^2)

\int \frac{6 + 3 x}{1 + x ^{2}} d x

integral of x^3(x+1)(x+2)

\int x^{3} (x + 1) (x + 2) d x

integral of (x+1)/(x^2-3x+4)

\int \frac{x + 1}{x ^{2} - 3 x + 4} d x

integral of sin(sqrt(1+2x))

\int sin (1 + 2 x) d x

Frequently Asked Questions (FAQ)

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