What is the integral of (2(x+2))/5 ?

The integral of (2(x+2))/5 is (x^2)/5+4/5 x+C

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integral of (2(x+2))/5

\int \frac{2 ( x + 2 )}{5} d x

\frac{x ^{2}}{5} + \frac{4}{5} x + C

Solution steps

\int \frac{2 ( x + 2 )}{5} d x

Take the constant out:

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

= \frac{2}{5} \cdot \int x + 2 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}{5} (\int x d x + \int 2 d x)

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

\int 2 d x = 2 x

= \frac{2}{5} (\frac{x ^{2}}{2} + 2 x)

Simplify

\frac{2}{5} (\frac{x ^{2}}{2} + 2 x) : \frac{x ^{2}}{5} + \frac{4}{5} x

= \frac{x ^{2}}{5} + \frac{4}{5} x

Add a constant to the solution

= \frac{x ^{2}}{5} + \frac{4}{5} x + C

f (x) = \frac{x ^{3} + 2}{3}, at x = - 3

\frac{d}{d x} (x^{4} + y^{4})

\frac{d}{d x} (\frac{x}{x ^{3} + 1})

f (x) = cos^{2} (2 x)

\frac{1 - 2 x}{1 + 2 x}

What is the integral of (2(x+2))/5 ?
The integral of (2(x+2))/5 is (x^2)/5+4/5 x+C