Integral of x+sqrt(x) dx

The solution

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$$\int\limits_{0}^{1} \left(\sqrt{x} + x\right)\, dx$$

Integral(x + sqrt(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
The result is: $\frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}$
Add the constant of integration:

$\frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}+ \mathrm{constant}$

The answer is:

$\frac{2 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
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 | \x + \/ x / dx = C + -- + ------
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$${{x^2}\over{2}}+{{2\,x^{{{3}\over{2}}}}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/6

$${{7}\over{6}}$$

7/6

$$\frac{7}{6}$$

Simplify

Numerical answer [src]

1.16666666666667

1.16666666666667

The graph

Use the examples entering the upper and lower limits of integration.

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Identical expressions

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Integral of x+sqrt(x) dx

Limits of integration:

The graph:

Piecewise:

The solution