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

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

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integral of x+1sqrt(x)

\int x + 1 x d x

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

Solution steps

\int x + 1 \cdot x d x

Simplify

= \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

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\frac{\partial}{\partial x} (\frac{sin ( x )}{r ^{2}})

\frac{d}{d x} (9 x^{l n (9 x)})

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