Mister Exam

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Integral of d{x}:
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Integral of x/(x^3+8)
Derivative of:
1+x^(1/2)
Identical expressions
one +x^(one / two)
1 plus x to the power of (1 divide by 2)
one plus x to the power of (one divide by two)
1+x(1/2)
1+x1/2
1+x^1/2
1+x^(1 divide by 2)
1+x^(1/2)dx
Similar expressions
1+x^1/2
1-x^(1/2)

Solving integrals/ 1+x^(1/2)

Integral of 1+x^(1/2) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |  /      ___\   
 |  \1 + \/ x / dx
 |                
/                 
0

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

Integral(1 + 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 a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{2 x^{\frac{3}{2}}}{3} + x$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                               
 |                             3/2
 | /      ___\              2*x   
 | \1 + \/ x / dx = C + x + ------
 |                            3   
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/3

$$\frac{5}{3}$$

5/3

$$\frac{5}{3}$$

5/3

Numerical answer [src]

1.66666666666667

1.66666666666667

The graph

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

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Identical expressions

Similar expressions

Integral of 1+x^(1/2) dx

Limits of integration:

The graph:

Piecewise:

The solution