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Identical expressions
7x^ six -5x+ three / two x^2
7x to the power of 6 minus 5x plus 3 divide by 2x squared
7x to the power of six minus 5x plus three divide by two x squared
7x6-5x+3/2x2
7x⁶-5x+3/2x²
7x to the power of 6-5x+3/2x to the power of 2
7x^6-5x+3 divide by 2x^2
7x^6-5x+3/2x^2dx
Similar expressions
7x^6+5x+3/2x^2
7x^6-5x-3/2x^2

Solving integrals/ 7x^6-5x+3/2x^2

Integral of 7x^6-5x+3/2x^2 dx

The solution

You have entered [src]

  1                       
  /                       
 |                        
 |  /                2\   
 |  |   6         3*x |   
 |  |7*x  - 5*x + ----| dx
 |  \              2  /   
 |                        
/                         
0

$$\int\limits_{0}^{1} \left(7 x^{6} + \frac{3 x^{2}}{2} - 5 x\right)\, dx$$

Integral(7*x^6 - 5*x + 3*x^2/2, (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:
  
  $\int 7 x^{6}\, dx = 7 \int x^{6}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{6}\, dx = \frac{x^{7}}{7}$
  So, the result is: $x^{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3 x^{2}}{2}\, dx = \frac{3 \int x^{2}\, dx}{2}$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $\frac{x^{3}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 5 x\right)\, dx = - \int 5 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    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: $\frac{5 x^{2}}{2}$
  So, the result is: $- \frac{5 x^{2}}{2}$
The result is: $x^{7} + \frac{x^{3}}{2} - \frac{5 x^{2}}{2}$
Now simplify:

$\frac{x^{2} \cdot \left(2 x^{5} + x - 5\right)}{2}$
Add the constant of integration:

$\frac{x^{2} \cdot \left(2 x^{5} + x - 5\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \cdot \left(2 x^{5} + x - 5\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                            
 | /                2\                3      2
 | |   6         3*x |           7   x    5*x 
 | |7*x  - 5*x + ----| dx = C + x  + -- - ----
 | \              2  /               2     2  
 |                                            
/

$$\int \left(7 x^{6} + \frac{3 x^{2}}{2} - 5 x\right)\, dx = C + x^{7} + \frac{x^{3}}{2} - \frac{5 x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1

$$-1$$

-1

$$-1$$

Упростить

Numerical answer [src]

-1.0

-1.0

The graph

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

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Integral of 7x^6-5x+3/2x^2 dx

Limits of integration:

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Piecewise:

The solution