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Identical expressions
(four *x^ four + six *x^ two - eight *x^ seven)dx
(4 multiply by x to the power of 4 plus 6 multiply by x squared minus 8 multiply by x to the power of 7)dx
(four multiply by x to the power of four plus six multiply by x to the power of two minus eight multiply by x to the power of seven)dx
(4*x4+6*x2-8*x7)dx
4*x4+6*x2-8*x7dx
(4*x⁴+6*x²-8*x⁷)dx
(4*x to the power of 4+6*x to the power of 2-8*x to the power of 7)dx
(4x^4+6x^2-8x^7)dx
(4x4+6x2-8x7)dx
4x4+6x2-8x7dx
4x^4+6x^2-8x^7dx
Similar expressions
(4*x^4+6*x^2+8*x^7)dx
(4*x^4-6*x^2-8*x^7)dx

Solving integrals/ (4*x^4+6*x^2-8*x^7)dx

Integral of (4x^4+6x^2-8*x^7)dx dx

The solution

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  1                        
  /                        
 |                         
 |  /   4      2      7\   
 |  \4*x  + 6*x  - 8*x / dx
 |                         
/                          
0

$$\int\limits_{0}^{1} \left(- 8 x^{7} + \left(4 x^{4} + 6 x^{2}\right)\right)\, dx$$

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

$x^{3} \left(- x^{5} + \frac{4 x^{2}}{5} + 2\right)$
Add the constant of integration:

$x^{3} \left(- x^{5} + \frac{4 x^{2}}{5} + 2\right)+ \mathrm{constant}$

The answer is:

$x^{3} \left(- x^{5} + \frac{4 x^{2}}{5} + 2\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(- 8 x^{7} + \left(4 x^{4} + 6 x^{2}\right)\right)\, dx = C - x^{8} + \frac{4 x^{5}}{5} + 2 x^{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

9/5

$$\frac{9}{5}$$

9/5

$$\frac{9}{5}$$

9/5

Numerical answer [src]

1.8

1.8

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 (4x^4+6x^2-8*x^7)dx dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (4*x^4+6*x^2-8*x^7)dx dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of (4x^4+6x^2-8*x^7)dx dx