What is the integral of (sqrt(8x)-2x) ?

The integral of (sqrt(8x)-2x) is (4sqrt(2))/3 x^{3/2}-x^2+C

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integral of (sqrt(8x)-2x)

\int (8 x - 2 x) d x

\frac{4 2}{3} x^{\frac{3}{2}} - x^{2} + C

Solution steps

\int 8 x - 2 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

= \int 8 x d x - \int 2 x d x

\int 8 x d x = \frac{4 2}{3} x^{\frac{3}{2}}

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

= \frac{4 2}{3} x^{\frac{3}{2}} - x^{2}

Add a constant to the solution

= \frac{4 2}{3} x^{\frac{3}{2}} - x^{2} + C

What is the integral of (sqrt(8x)-2x) ?
The integral of (sqrt(8x)-2x) is (4sqrt(2))/3 x^{3/2}-x^2+C