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Popular >

integral of-x/3

Solution

\int - \frac{x}{3} d x

Solution

- \frac{x ^{2}}{6} + C

Solution steps

\int - \frac{x}{3} d x

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

- \frac{1}{3} \cdot \frac{x ^{2}}{2} : - \frac{x ^{2}}{6}

= - \frac{x ^{2}}{6}

Add a constant to the solution

= - \frac{x ^{2}}{6} + C

Popular Examples

derivative of-sin(2x2)

\frac{d}{d x} (- sin (2 x) 2)

(x-1)y^'+(x-2)y=0

(x - 1) y^{^{'}} + (x - 2) y = 0

derivative of-2cos(sqrt(x))

\frac{d}{d x} (- 2 cos (x))

yln(x)ln(y)dx+dy=0

y ln (x) ln (y) d x + d y = 0

integral of (2^x)/(3^x)

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

Frequently Asked Questions (FAQ)

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