Integral of sqrtx+sqrtx+1 dx

The solution

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0

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

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

Detail solution

Integrate term-by-term:
1. 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 $n \neq -1$ :
    
    $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
  The result is: $\frac{4 x^{\frac{3}{2}}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{4 x^{\frac{3}{2}}}{3} + x$
Add the constant of integration:

$\frac{4 x^{\frac{3}{2}}}{3} + x+ \mathrm{constant}$

The answer is:

$\frac{4 x^{\frac{3}{2}}}{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
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 | /  ___     ___    \              4*x   
 | \\/ x  + \/ x  + 1/ dx = C + x + ------
 |                                    3   
/

$$\int \left(\left(\sqrt{x} + \sqrt{x}\right) + 1\right)\, dx = C + \frac{4 x^{\frac{3}{2}}}{3} + x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

7/3

$$\frac{7}{3}$$

7/3

$$\frac{7}{3}$$

7/3

Numerical answer [src]

2.33333333333333

2.33333333333333

The graph

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

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Integral of sqrtx+sqrtx+1 dx

Limits of integration:

The graph:

Piecewise:

The solution