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Popular >

integral of-2/3 x

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

integral of 20sin(x)

\int 20 sin (x) d x

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

integral of (sin(46x))/(1+cos^2(46x))

\int \frac{sin ( 46 x )}{1 + cos ^{2} ( 46 x )} d x

integral of (x^7-5x)/(x^6)

\int \frac{x ^{7} - 5 x}{x ^{6}} d x

integral of 2xsin(npix)

\int 2 x sin (nπ x) d x

Frequently Asked Questions (FAQ)

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