What is the integral of (2(1+x))/(27) ?

The integral of (2(1+x))/(27) is 2/27 x+(x^2)/(27)+C

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integral of (2(1+x))/(27)

\int \frac{2 ( 1 + x )}{27} d x

\frac{2}{27} x + \frac{x ^{2}}{27} + C

Solution steps

\int \frac{2 ( 1 + x )}{27} d x

Take the constant out:

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

= \frac{2}{27} \cdot \int 1 + x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{2}{27} (\int 1 d x + \int x d x)

\int 1 d x = x

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

= \frac{2}{27} (x + \frac{x ^{2}}{2})

Simplify

\frac{2}{27} (x + \frac{x ^{2}}{2}) : \frac{2}{27} x + \frac{x ^{2}}{27}

= \frac{2}{27} x + \frac{x ^{2}}{27}

Add a constant to the solution

= \frac{2}{27} x + \frac{x ^{2}}{27} + C

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What is the integral of (2(1+x))/(27) ?
The integral of (2(1+x))/(27) is 2/27 x+(x^2)/(27)+C