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

f (t) = 3 t sin (π t)

\int 3 x \cdot 2^{x^{2}} d x

x \to 0 lim (\frac{sin ( x )}{3 x})

x^{3} + y^{3} = 7 x y, (2, - 4)

y = \frac{1}{x ^{2}}, (- 1, 1)

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