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Integral of (x^6-7x)^4dx
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Integral of r^2dr
Identical expressions
(x^ six -7x)^4dx
(x to the power of 6 minus 7x) to the power of 4dx
(x to the power of six minus 7x) to the power of 4dx
(x6-7x)4dx
x6-7x4dx
(x⁶-7x)⁴dx
x^6-7x^4dx
Similar expressions
(x^6+7x)^4dx

Solving integrals/ (x^6-7x)^4dx

Integral of (x^6-7x)^4dx dx

The solution

You have entered [src]

  3                 
  /                 
 |                  
 |            4     
 |  / 6      \      
 |  \x  - 7*x/ *1 dx
 |                  
/                   
0

\int\limits_{0}^{3} \left(x^{6} - 7 x\right)^{4} \cdot 1\, dx

Integral((x^6 - 7*x)^4*1, (x, 0, 3))

Detail solution

Rewrite the integrand:

$\left(x^{6} - 7 x\right)^{4} \cdot 1 = x^{24} - 28 x^{19} + 294 x^{14} - 1372 x^{9} + 2401 x^{4}$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{24}\, dx = \frac{x^{25}}{25}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 28 x^{19}\right)\, dx = - 28 \int x^{19}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{19}\, dx = \frac{x^{20}}{20}$
  So, the result is: $- \frac{7 x^{20}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 294 x^{14}\, dx = 294 \int x^{14}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{14}\, dx = \frac{x^{15}}{15}$
  So, the result is: $\frac{98 x^{15}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 1372 x^{9}\right)\, dx = - 1372 \int x^{9}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{9}\, dx = \frac{x^{10}}{10}$
  So, the result is: $- \frac{686 x^{10}}{5}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2401 x^{4}\, dx = 2401 \int x^{4}\, dx$
  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: $\frac{2401 x^{5}}{5}$
The result is: $\frac{x^{25}}{25} - \frac{7 x^{20}}{5} + \frac{98 x^{15}}{5} - \frac{686 x^{10}}{5} + \frac{2401 x^{5}}{5}$
Now simplify:

$\frac{x^{5} \left(x^{20} - 35 x^{15} + 490 x^{10} - 3430 x^{5} + 12005\right)}{25}$
Add the constant of integration:

$\frac{x^{5} \left(x^{20} - 35 x^{15} + 490 x^{10} - 3430 x^{5} + 12005\right)}{25}+ \mathrm{constant}$

The answer is:

\frac{x^{5} \left(x^{20} - 35 x^{15} + 490 x^{10} - 3430 x^{5} + 12005\right)}{25}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                                                               
 |                                                                
 |           4                 10      20    25       15         5
 | / 6      \             686*x     7*x     x     98*x     2401*x 
 | \x  - 7*x/ *1 dx = C - ------- - ----- + --- + ------ + -------
 |                           5        5      25     5         5   
/

\int \left(x^{6} - 7 x\right)^{4} \cdot 1\, dx = C + \frac{x^{25}}{25} - \frac{7 x^{20}}{5} + \frac{98 x^{15}}{5} - \frac{686 x^{10}}{5} + \frac{2401 x^{5}}{5}

Simplify

The graph

Plot the graph f(x)

The answer [src]

732082498983
------------
     25

\frac{732082498983}{25}

732082498983
------------
     25

\frac{732082498983}{25}

Упростить

Numerical answer [src]

29283299959.32

29283299959.32

The graph

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

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Integral of (x^6-7x)^4dx dx

Limits of integration:

The graph:

Piecewise:

The solution