What is the integral of (4x-2sqrt(x)) ?

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

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integral of (4x-2sqrt(x))

\int (4 x - 2 x) d x

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

Solution steps

\int 4 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 4 x d x - \int 2 x d x

\int 4 x d x = 2 x^{2}

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

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

Add a constant to the solution

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

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