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Identical expressions
four , five + three , five *x+x^(three / two)
4,5 plus 3,5 multiply by x plus x to the power of (3 divide by 2)
four , five plus three , five multiply by x plus x to the power of (three divide by two)
4,5+3,5*x+x(3/2)
4,5+3,5*x+x3/2
4,5+3,5x+x^(3/2)
4,5+3,5x+x(3/2)
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4,5+3,5x+x^3/2
4,5+3,5*x+x^(3 divide by 2)
4,5+3,5*x+x^(3/2)dx
Similar expressions
4,5-3,5*x+x^(3/2)
4,5+3,5*x-x^(3/2)

Solving integrals/ 4,5+3,5*x+x^(3/2)

Integral of 4,5+3,5*x+x^(3/2) dx

The solution

You have entered [src]

  1                    
  /                    
 |                     
 |  /9   7*x    3/2\   
 |  |- + --- + x   | dx
 |  \2    2        /   
 |                     
/                      
0

$$\int\limits_{0}^{1} \left(x^{\frac{3}{2}} + \frac{7 x}{2} + \frac{9}{2}\right)\, dx$$

Integral(9/2 + 7*x/2 + x^(3/2), (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{\frac{3}{2}}\, dx = \frac{2 x^{\frac{5}{2}}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{7 x}{2}\, dx = \frac{7 \int x\, dx}{2}$
  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: $\frac{7 x^{2}}{4}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \frac{9}{2}\, dx = \frac{9 x}{2}$
The result is: $\frac{2 x^{\frac{5}{2}}}{5} + \frac{7 x^{2}}{4} + \frac{9 x}{2}$
Add the constant of integration:

$\frac{2 x^{\frac{5}{2}}}{5} + \frac{7 x^{2}}{4} + \frac{9 x}{2}+ \mathrm{constant}$

The answer is:

$\frac{2 x^{\frac{5}{2}}}{5} + \frac{7 x^{2}}{4} + \frac{9 x}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                             
 |                              5/2      2      
 | /9   7*x    3/2\          2*x      7*x    9*x
 | |- + --- + x   | dx = C + ------ + ---- + ---
 | \2    2        /            5       4      2 
 |                                              
/

$${{2\,x^{{{5}\over{2}}}}\over{5}}+{{7\,x^2}\over{4}}+{{9\,x}\over{2 }}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

133
---
 20

$${{133}\over{20}}$$

133
---
 20

$$\frac{133}{20}$$

Упростить

Numerical answer [src]

6.65

6.65

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 4,5+3,5*x+x^(3/2) dx

Limits of integration:

The graph:

Piecewise:

The solution