What is the integral of sqrt(x)+1 ?

The integral of sqrt(x)+1 is 2/3 x^{3/2}+x+C

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integral of sqrt(x)+1

\int x + 1 d x

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

Solution steps

\int x + 1 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 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

x \to 0 lim (\frac{4}{x ^{3} ( x + 3 )})

sin (x), 1

\frac{x ^{2}}{28}

\frac{d}{d x} (cos (2 x) + sin (2 x))

x^{2} + x + 3

What is the integral of sqrt(x)+1 ?
The integral of sqrt(x)+1 is 2/3 x^{3/2}+x+C