What is the integral of 3x-2sqrt(x) ?

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

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integral of 3x-2sqrt(x)

\int 3 x - 2 x d x

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

Solution steps

\int 3 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 3 x d x - \int 2 x d x

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

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

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

Add a constant to the solution

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

\frac{\partial}{\partial y} (y e^{x y})

\frac{d}{d x} (f (x) g (x) h (x))

x \to 0 lim (sin (1))

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

(- 1, 6), (2, - 3)

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