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

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

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integral of sqrt(x)-2

\int x - 2 d x

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

Solution steps

\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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\frac{d y}{d x} = y (4 x^{2} + 6)

y^{^{''}} - 6 y^{^{'}} + 3 y = 0, y (0) = 0, y^{^{'}} (0) = 5

y^{^{'}} = \frac{( 3 x ^{2} - e ^{x} )}{( 2 y - 5 )}

h \to 0 lim (\frac{( 3 + h ) ^{2} - 9}{h})

(\frac{d y}{d t}) = 2 (y^{2} - y) t

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