What is the integral of sqrt(x)+3 ?

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

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integral of sqrt(x)+3

\int x + 3 d x

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

Solution steps

\int x + 3 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 3 d x

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (e^{x} y + 5 x y^{2} - x^{2})

n = 0 \sum \infty \frac{3}{n ^{4}}

\frac{d}{d x} (x cos (x) - sin (x))

\int sin (t) cos (n t) d t

y^{^{''}} - 3 y^{^{'}} = e^{3 t}

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