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

\int e^{2} ln (x) d x

\int \frac{x}{1 - 9 x ^{2}} d x

x \to 4 lim (\frac{∣ 4 - x ∣}{4 - x})

\int (2 x^{- 1}) d x

2 y^{^{''}} + y^{^{'}} - 3 y = 0

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