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

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

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integral of x+sqrt(x)

\int x + x d x

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

Solution steps

\int x + x 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 x d x

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

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

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

Add a constant to the solution

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

f (x) = 3 x + \frac{2}{x}, at x = 2

\frac{d y}{d x} + 7 x^{6} y = x^{6}

\frac{2 x + 4 x ^{2}}{( 1 + 4 x ) ^{2}}

\frac{d}{d x} (e^{k^{2} x})

\frac{d}{d x} (\frac{( x + 4 ) ^{2}}{x + 3})

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