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Identical expressions
one /2x+ five *sqrt(x)
1 divide by 2x plus 5 multiply by square root of (x)
one divide by 2x plus five multiply by square root of (x)
1/2x+5*√(x)
1/2x+5sqrt(x)
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1 divide by 2x+5*sqrt(x)
1/2x+5*sqrt(x)dx
Similar expressions
1/2x-5*sqrt(x)

Integral of 1/2x+5*sqrt(x) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |  /x       ___\   
 |  |- + 5*\/ x | dx
 |  \2          /   
 |                  
/                   
0

$$\int\limits_{0}^{1} \left(5 \sqrt{x} + \frac{x}{2}\right)\, dx$$

Integral(x/2 + 5*sqrt(x), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 \sqrt{x}\, dx = 5 \int \sqrt{x}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{x}\, dx = \frac{2 x^{\frac{3}{2}}}{3}$
  So, the result is: $\frac{10 x^{\frac{3}{2}}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{x}{2}\, dx = \frac{\int x\, dx}{2}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{x^{2}}{4}$
The result is: $\frac{10 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{4}$
Add the constant of integration:

$\frac{10 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{4}+ \mathrm{constant}$

The answer is:

$\frac{10 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                         2       3/2
 | /x       ___\          x    10*x   
 | |- + 5*\/ x | dx = C + -- + -------
 | \2          /          4       3   
 |                                    
/

$$\int \left(5 \sqrt{x} + \frac{x}{2}\right)\, dx = C + \frac{10 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

43
--
12

$$\frac{43}{12}$$

43
--
12

$$\frac{43}{12}$$

43/12

Numerical answer [src]

3.58333333333333

3.58333333333333

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

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Integral of 1/2x+5*sqrt(x) dx

Limits of integration:

The graph:

Piecewise:

The solution