What is the integral of sqrt(x)+4 ?

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

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integral of sqrt(x)+4

\int x + 4 d x

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

Solution steps

\int x + 4 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 4 d x

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

\int p^{2} ln (p) d p

x \to 0 lim (x^{2} - 2 x)

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

f (x) = \frac{1}{x}, at x = 0.501

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