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Identical expressions
six x^6-8x^ three + five
6x to the power of 6 minus 8x cubed plus 5
six x to the power of 6 minus 8x to the power of three plus five
6x6-8x3+5
6x⁶-8x³+5
6x to the power of 6-8x to the power of 3+5
6x^6-8x^3+5dx
Similar expressions
6x^6+8x^3+5
6x^6-8x^3-5

Solving integrals/ 6x^6-8x^3+5

Integral of 6x^6-8x^3+5 dx

The solution

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  1                     
  /                     
 |                      
 |  /   6      3    \   
 |  \6*x  - 8*x  + 5/ dx
 |                      
/                       
0

$$\int\limits_{0}^{1} \left(6 x^{6} - 8 x^{3} + 5\right)\, dx$$

Integral(6*x^6 - 8*x^3 + 5, (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:
  
  $\int 6 x^{6}\, dx = 6 \int x^{6}\, dx$
  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: $\frac{6 x^{7}}{7}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 8 x^{3}\right)\, dx = - \int 8 x^{3}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 8 x^{3}\, dx = 8 \int x^{3}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{3}\, dx = \frac{x^{4}}{4}$
    So, the result is: $2 x^{4}$
  So, the result is: $- 2 x^{4}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 5\, dx = 5 x$
The result is: $\frac{6 x^{7}}{7} - 2 x^{4} + 5 x$
Now simplify:

$\frac{x \left(6 x^{6} - 14 x^{3} + 35\right)}{7}$
Add the constant of integration:

$\frac{x \left(6 x^{6} - 14 x^{3} + 35\right)}{7}+ \mathrm{constant}$

The answer is:

$\frac{x \left(6 x^{6} - 14 x^{3} + 35\right)}{7}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                            
 |                                            7
 | /   6      3    \             4         6*x 
 | \6*x  - 8*x  + 5/ dx = C - 2*x  + 5*x + ----
 |                                          7  
/

$${{6\,x^7}\over{7}}-2\,x^4+5\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

27/7

$${{27}\over{7}}$$

27/7

$$\frac{27}{7}$$

Упростить

Numerical answer [src]

3.85714285714286

3.85714285714286

The graph

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

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Integral of 6x^6-8x^3+5 dx

Limits of integration:

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Piecewise:

The solution