What is the integral of y= x/(2+1) ?

The integral of y= x/(2+1) is (x^2)/6+C

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integral of y= x/(2+1)

integral

y = \frac{x}{2 + 1}

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

Solution steps

\int \frac{x}{2 + 1} d x

Take the constant out:

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

= \frac{1}{2 + 1} \cdot \int x d x

Simplify

= \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

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

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

\frac{1 + x}{1 - x}

(1 - x)^{5}

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