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}{d x} (\frac{3 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}})

y^{^{''}} + 2 y^{^{'}} + y = - 2 e^{x}

\frac{d y}{d x} = \frac{x - 4}{y - 6}

\int_{1}^{2} \frac{5}{x ^{3} + 2 x} d x

\int_{0}^{1} (5^{x} - 3^{x}) d x

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